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? show work

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

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