div class=ts-pagebutton class=gotoPage data-page=1Page 1button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=1 data-page=1 class=ts-thumb lazyload alt=Page 1: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails1jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=2Page 2button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=2 data-page=2 class=ts-thumb lazyload alt=Page 2: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails2jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=3Page 3button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=3 data-page=3 class=ts-thumb lazyload alt=Page 3: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails3jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=4Page 4button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=4 data-page=4 class=ts-thumb lazyload alt=Page 4: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails4jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=5Page 5button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=5 data-page=5 class=ts-thumb lazyload alt=Page 5: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails5jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=6Page 6button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=6 data-page=6 class=ts-thumb lazyload alt=Page 6: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails6jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=7Page 7button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=7 data-page=7 class=ts-thumb lazyload alt=Page 7: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails7jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=8Page 8button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=8 data-page=8 class=ts-thumb lazyload alt=Page 8: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails8jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=9Page 9button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=9 data-page=9 class=ts-thumb lazyload alt=Page 9: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails9jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=10Page 10button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=10 data-page=10 class=ts-thumb lazyload alt=Page 10: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails10jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=11Page 11button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=11 data-page=11 class=ts-thumb lazyload alt=Page 11: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails11jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=12Page 12button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=12 data-page=12 class=ts-thumb lazyload alt=Page 12: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails12jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=13Page 13button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=13 data-page=13 class=ts-thumb lazyload alt=Page 13: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails13jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=14Page 14button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=14 data-page=14 class=ts-thumb lazyload alt=Page 14: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails14jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=15Page 15button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=15 data-page=15 class=ts-thumb lazyload alt=Page 15: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails15jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=16Page 16button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=16 data-page=16 class=ts-thumb lazyload alt=Page 16: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails16jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=17Page 17button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=17 data-page=17 class=ts-thumb lazyload alt=Page 17: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails17jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=18Page 18button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=18 data-page=18 class=ts-thumb lazyload alt=Page 18: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails18jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=19Page 19button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=19 data-page=19 class=ts-thumb lazyload alt=Page 19: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails19jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=20Page 20button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=20 data-page=20 class=ts-thumb lazyload alt=Page 20: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails20jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=21Page 21button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=21 data-page=21 class=ts-thumb lazyload alt=Page 21: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails21jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=22Page 22button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=22 data-page=22 class=ts-thumb lazyload alt=Page 22: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails22jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=23Page 23button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=23 data-page=23 class=ts-thumb lazyload alt=Page 23: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails23jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=24Page 24button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=24 data-page=24 class=ts-thumb lazyload alt=Page 24: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails24jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=25Page 25button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=25 data-page=25 class=ts-thumb lazyload alt=Page 25: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails25jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=26Page 26button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=26 data-page=26 class=ts-thumb lazyload alt=Page 26: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails26jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=27Page 27button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=27 data-page=27 class=ts-thumb lazyload alt=Page 27: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails27jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=28Page 28button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=28 data-page=28 class=ts-thumb lazyload alt=Page 28: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails28jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=29Page 29button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=29 data-page=29 class=ts-thumb lazyload alt=Page 29: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails29jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=30Page 30button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=30 data-page=30 class=ts-thumb lazyload alt=Page 30: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails30jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=31Page 31button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=31 data-page=31 class=ts-thumb lazyload alt=Page 31: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails31jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=32Page 32button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=32 data-page=32 class=ts-thumb lazyload alt=Page 32: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails32jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=33Page 33button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=33 data-page=33 class=ts-thumb lazyload alt=Page 33: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails33jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=34Page 34button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=34 data-page=34 class=ts-thumb lazyload alt=Page 34: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails34jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=35Page 35button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=35 data-page=35 class=ts-thumb lazyload alt=Page 35: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails35jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=36Page 36button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=36 data-page=36 class=ts-thumb lazyload alt=Page 36: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails36jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=37Page 37button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=37 data-page=37 class=ts-thumb lazyload alt=Page 37: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails37jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=38Page 38button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=38 data-page=38 class=ts-thumb lazyload alt=Page 38: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails38jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=39Page 39button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=39 data-page=39 class=ts-thumb lazyload alt=Page 39: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails39jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=40Page 40button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=40 data-page=40 class=ts-thumb lazyload alt=Page 40: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails40jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=41Page 41button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=41 data-page=41 class=ts-thumb lazyload alt=Page 41: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails41jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=42Page 42button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=42 data-page=42 class=ts-thumb lazyload alt=Page 42: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails42jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=43Page 43button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=43 data-page=43 class=ts-thumb lazyload alt=Page 43: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails43jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=44Page 44button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=44 data-page=44 class=ts-thumb lazyload alt=Page 44: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails44jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=45Page 45button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=45 data-page=45 class=ts-thumb lazyload alt=Page 45: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails45jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=46Page 46button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=46 data-page=46 class=ts-thumb lazyload alt=Page 46: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails46jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=47Page 47button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=47 data-page=47 class=ts-thumb lazyload alt=Page 47: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails47jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=48Page 48button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=48 data-page=48 class=ts-thumb lazyload alt=Page 48: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails48jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=49Page 49button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=49 data-page=49 class=ts-thumb lazyload alt=Page 49: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails49jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=50Page 50button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=50 data-page=50 class=ts-thumb lazyload alt=Page 50: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails50jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=51Page 51button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=51 data-page=51 class=ts-thumb lazyload alt=Page 51: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails51jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=52Page 52button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=52 data-page=52 class=ts-thumb lazyload alt=Page 52: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails52jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=53Page 53button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=53 data-page=53 class=ts-thumb lazyload alt=Page 53: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails53jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=54Page 54button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=54 data-page=54 class=ts-thumb lazyload alt=Page 54: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails54jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=55Page 55button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=55 data-page=55 class=ts-thumb lazyload alt=Page 55: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails55jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=56Page 56button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=56 data-page=56 class=ts-thumb lazyload alt=Page 56: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails56jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=57Page 57button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=57 data-page=57 class=ts-thumb lazyload alt=Page 57: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails57jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=58Page 58button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=58 data-page=58 class=ts-thumb lazyload alt=Page 58: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails58jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=59Page 59button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=59 data-page=59 class=ts-thumb lazyload alt=Page 59: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails59jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=60Page 60button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=60 data-page=60 class=ts-thumb lazyload alt=Page 60: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails60jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=61Page 61button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=61 data-page=61 class=ts-thumb lazyload alt=Page 61: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails61jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=62Page 62button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=62 data-page=62 class=ts-thumb lazyload alt=Page 62: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails62jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=63Page 63button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=63 data-page=63 class=ts-thumb lazyload alt=Page 63: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails63jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=64Page 64button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=64 data-page=64 class=ts-thumb lazyload alt=Page 64: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails64jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=65Page 65button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=65 data-page=65 class=ts-thumb lazyload alt=Page 65: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails65jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=66Page 66button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=66 data-page=66 class=ts-thumb lazyload alt=Page 66: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails66jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=67Page 67button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=67 data-page=67 class=ts-thumb lazyload alt=Page 67: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails67jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=68Page 68button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=68 data-page=68 class=ts-thumb lazyload alt=Page 68: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails68jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=69Page 69button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=69 data-page=69 class=ts-thumb lazyload alt=Page 69: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails69jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=70Page 70button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=70 data-page=70 class=ts-thumb lazyload alt=Page 70: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails70jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=71Page 71button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=71 data-page=71 class=ts-thumb lazyload alt=Page 71: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails71jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=72Page 72button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=72 data-page=72 class=ts-thumb lazyload alt=Page 72: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails72jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=73Page 73button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=73 data-page=73 class=ts-thumb lazyload alt=Page 73: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails73jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=74Page 74button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=74 data-page=74 class=ts-thumb lazyload alt=Page 74: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails74jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=75Page 75button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=75 data-page=75 class=ts-thumb lazyload alt=Page 75: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails75jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=76Page 76button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=76 data-page=76 class=ts-thumb lazyload alt=Page 76: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails76jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=77Page 77button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=77 data-page=77 class=ts-thumb lazyload alt=Page 77: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails77jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=78Page 78button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=78 data-page=78 class=ts-thumb lazyload alt=Page 78: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails78jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=79Page 79button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=79 data-page=79 class=ts-thumb lazyload alt=Page 79: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails79jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=80Page 80button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=80 data-page=80 class=ts-thumb lazyload alt=Page 80: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails80jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=81Page 81button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=81 data-page=81 class=ts-thumb lazyload alt=Page 81: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails81jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=82Page 82button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=82 data-page=82 class=ts-thumb lazyload alt=Page 82: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails82jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=83Page 83button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=83 data-page=83 class=ts-thumb lazyload alt=Page 83: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails83jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=84Page 84button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=84 data-page=84 class=ts-thumb lazyload alt=Page 84: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails84jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=85Page 85button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=85 data-page=85 class=ts-thumb lazyload alt=Page 85: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails85jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=86Page 86button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=86 data-page=86 class=ts-thumb lazyload alt=Page 86: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails86jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=87Page 87button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=87 data-page=87 class=ts-thumb lazyload alt=Page 87: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails87jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=88Page 88button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=88 data-page=88 class=ts-thumb lazyload alt=Page 88: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails88jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=89Page 89button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=89 data-page=89 class=ts-thumb lazyload alt=Page 89: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails89jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=90Page 90button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=90 data-page=90 class=ts-thumb lazyload alt=Page 90: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails90jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=91Page 91button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=91 data-page=91 class=ts-thumb lazyload alt=Page 91: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails91jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=92Page 92button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=92 data-page=92 class=ts-thumb lazyload alt=Page 92: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails92jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=93Page 93button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=93 data-page=93 class=ts-thumb lazyload alt=Page 93: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails93jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=94Page 94button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=94 data-page=94 class=ts-thumb lazyload alt=Page 94: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails94jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=95Page 95button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=95 data-page=95 class=ts-thumb lazyload alt=Page 95: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails95jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=96Page 96button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=96 data-page=96 class=ts-thumb lazyload alt=Page 96: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails96jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=97Page 97button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=97 data-page=97 class=ts-thumb lazyload alt=Page 97: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails97jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=98Page 98button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=98 data-page=98 class=ts-thumb lazyload alt=Page 98: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails98jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=99Page 99button div class=ts-imageimg data-url=units-1-the-orthogonal-gradient-theorem-is-key-to-lagrange-multipliers-supposehtmlpage=99 data-page=99 class=ts-thumb lazyload alt=Page 99: Units 1 - 4efpubspdlouisvilleeduclasses201docsENGR201-Unit-04pdfThe Orthogonal Gradient Theorem is key to LaGrange Multipliers Suppose f x y z and gx y z are differentiable loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader033vdocumentsusreader033viewer20220530165f17661a80126a5d8f31144fhtml5thumbnails99jpg width=140 height=200 divdiv