11x1 t12 01 first derivative (2010)
TRANSCRIPT
![Page 1: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/1.jpg)
Geometrical Applications
of Differentiation The First Derivative
![Page 2: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/2.jpg)
Geometrical Applications
of Differentiation The First Derivative
dx
dyxf
dx
dxfy ,,,
![Page 3: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/3.jpg)
Geometrical Applications
of Differentiation The First Derivative
dx
dyxf
dx
dxfy ,,,
curve a o tangent t theof slope themeasures dx
dy
![Page 4: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/4.jpg)
Geometrical Applications
of Differentiation The First Derivative
dx
dyxf
dx
dxfy ,,,
curve a o tangent t theof slope themeasures dx
dy
increasing is curve the,0 If xf
![Page 5: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/5.jpg)
Geometrical Applications
of Differentiation The First Derivative
dx
dyxf
dx
dxfy ,,,
curve a o tangent t theof slope themeasures dx
dy
increasing is curve the,0 If xf
decreasing is curve the,0 If xf
![Page 6: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/6.jpg)
Geometrical Applications
of Differentiation The First Derivative
dx
dyxf
dx
dxfy ,,,
curve a o tangent t theof slope themeasures dx
dy
increasing is curve the,0 If xf
decreasing is curve the,0 If xf
stationary is curve the,0 If xf
![Page 7: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/7.jpg)
Geometrical Applications
of Differentiation The First Derivative
dx
dyxf
dx
dxfy ,,,
curve a o tangent t theof slope themeasures dx
dy
increasing is curve the,0 If xf
curve sketch the Hence
nature. their determine and
points stationary theof all find ,3 curve For the e.g. 32 xxy
decreasing is curve the,0 If xf
stationary is curve the,0 If xf
![Page 8: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/8.jpg)
Geometrical Applications
of Differentiation The First Derivative
dx
dyxf
dx
dxfy ,,,
curve a o tangent t theof slope themeasures dx
dy
increasing is curve the,0 If xf
curve sketch the Hence
nature. their determine and
points stationary theof all find ,3 curve For the e.g. 32 xxy
decreasing is curve the,0 If xf
stationary is curve the,0 If xf
236 xxdx
dy
![Page 9: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/9.jpg)
0 occur when points Stationary dx
dy
![Page 10: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/10.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
![Page 11: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/11.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
![Page 12: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/12.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
![Page 13: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/13.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
![Page 14: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/14.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
![Page 15: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/15.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
![Page 16: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/16.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
![Page 17: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/17.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0
![Page 18: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/18.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0
![Page 19: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/19.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1)
![Page 20: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/20.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1)
(-9)
![Page 21: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/21.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9)
![Page 22: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/22.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
![Page 23: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/23.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
![Page 24: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/24.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
2,4
![Page 25: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/25.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
2,4
x
dx
dy
![Page 26: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/26.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
2,4
x
dx
dy
2
![Page 27: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/27.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
2,4
x
dx
dy
2
0
![Page 28: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/28.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
2,4
x
dx
dy
2
0
2
![Page 29: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/29.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
2,4
x
dx
dy
2
0
2 2
![Page 30: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/30.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
2,4
x
dx
dy
2
0
2 2(1)
![Page 31: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/31.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
2,4
x
dx
dy
2
0
2 2(1)
(3)
![Page 32: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/32.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
2,4
x
dx
dy
2
0
2 2(1) (3)
(3)
![Page 33: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/33.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
2,4
x
dx
dy
2
0
2 2(1) (3)
(3) (-9)
![Page 34: 11X1 T12 01 first derivative (2010)](https://reader031.vdocuments.us/reader031/viewer/2022021814/58eed5c81a28ab574d8b462b/html5/thumbnails/34.jpg)
0 occur when points Stationary dx
dy
036 .. 2 xxei
2or 0
023
xx
xx
2,4 and 0,0at occur points stationary
0,0
x
dx
dy
0
0
0 0(-1) (1)
(-9) (3)
point turningminimum a is 0,0
2,4
x
dx
dy
2
0
2 2(1) (3)
(3) (-9)
point turningmaximum a is 2,4
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x
y
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x
y
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x
y
2,4
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x
y
2,4
323 xxy
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Exercise 10A; 1, 2ace, 4, 5, 6ac, 7, 8, 9ace etc,
11, 12, 13, 15ace, 16, 17
Exercise 10B; 1ad, 2ac, 3ac, 5, 6, 7ac, 8, 10, 12