if you graph this function, what is the maximum point?

Question

john is building a puppy pen in his backyard. He is going to use the corner of his existing fence as two of the sides of the pen, and has 40 feet of fencing material which will make up the other two sides of the pen. 

Answer 1

a square maximizes the are for a given amount of fence

A = LW = (40-W)W = 40W-W^2

A'(W) = 40-2W = 0

2W = 40

W = 40/2 = 20 feet wide

L=40-20 = 20 feet long

maximum area = 20(20) = 400 ft.^2