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23 August, 11:20

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

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Answers (1)
  1. 23 August, 11:46
    0
    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
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