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?

Answer 1

A = 24x - x^2

Finding the derivative:-

A' = 24 - 2x = 0 ( for minm/maxm)

2x = 24

x = 12 feet

A" is -2 so this is a maximum

Width for maximum area = 12 feet

length of the dog pen = (48 - 2(12) / 2 = 12 feet

so Maximum area = 12^2 = 144 ft^2