Suppose you have 54 feet of fencing to enclose a rectangular dog pen. The function a=27x-x^2, where x=width, gives you the area of the dog pen in square feet. What width gives you the maximum area? Round to the nearest tenth as necessary.
For maximum area, we take first derivative and then equalize it to zero A(x) = 27x- x^2 A'(x) = 27 - 2x
Set that equal to zero and solve for x : 27 - 2x = 0 27 = 2x ......................... [ added 2x to both sides ] 13.5 = x ........................ [ divided both sides by 2 ]
So the area will be A = 27(13.5) - (13.5)^2 = 364.5 - 182.25 = 182.3 ft^2
