Question

Suppose you have 48 feet of fencing to enclose a rectangular dog pen. The function

A = 24x-x2, where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area?
PLEASE SHOW WORK

Answer 1

Take first derivative of area function and set it to zero

da/dx=24 - 2x=0

Now it is set to zero add -2x to both side

24 - 2x = 0

24 = 2x

Now divide by 2 in both sides

12 = Width

Your width now is 12

Plug 12 into you equation like this:

24 (12) - 12^2= A

288 - 144 = A

144 = Area

144 feets is the maximum area using the width 24