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
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
