Question

Suppose you have 76 feet of fencing to enclose a rectangular dog pen. The function A = 38x – 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? Round to the nearest tenth as necessary.

Answer 1

Given that the area is defined by the function
$A=38x-x^2$

For maximum area, 
$\frac{dA}{dx} =0 \\ \\ 38-2x=0 \\ \\ 2x=38 \\ \\ x=19$

Therefore, the width that gives the maximum area is 19 feet.

The maximum area is given by
$A=38(19)-(19)^2 \\ \\ =19(38-19) \\ \\ =19(19)=361 \ square \, feet.$