http://www.analyzemath.com/calculus/Problems/optimize_area.html

http://mathdemos.gcsu.edu/mathdemos/penjava/pen.html

Section 19K

Recall: The max/min of a function occurs when the derivative =0

Ex. #1) Find the dimensions of a rectangle with maximum area if the perimeter must be 1000 meters. Find the maximum area. (Hint: Label all the sides according to one variable) 62,500 m2

Ex. #2) We need to enclose a field with a fence.  We have 500 feet of fencing material and a building is on one side of the field so you won’t need any fencing on that side.  Determine the dimensions of the field that will enclose the largest area and find the maximum area.

250ft x 125ft = 31,250ft2

Ex. #3) A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest size that will give a maximum volume.

box_folding.ggb

2ft x 2ft x ½ ft = 2ft3

Ex. #4) We have a piece of cardboard that is 14 inches by 10 inches and we’re going to cut out the corners as shown below and fold up the sides to form a box, also shown below.  Determine the height of the box that will give a maximum volume.

1.92 in

Pg. 634 #4