Question

Suppose you have 74 feet of fencing to enclose a rectangular dog pen. the function A=37x-x^2, 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?

A). width = 37ft; area =721.5
B). width = 18.5ft; area = 342.3
C). width = 37ft; area = 342.3
D). width = 18.5ft; area =1026.8

Answer 1

Answer:B). width = 18.5ft; area = 342.3

Explanation:

Answer 2

to solve for the maximum area, the first derivative should be solved and equate it to zero, then solve for x.
A = 37x - x^2
dA / dx = 37 - 2x
equate dA / dx = 0
0 = 37 - 2x
2x = 37
x = 37 / 2
x = 18.5 ft

so the maximum area is
A = 37x - x^2
A = 37( 18.5) - 18.5^2
A = 342.25 sq ft
so the answer is letter B