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Math Help - Area Problem

  1. #1
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    Area Problem

    If 300 feet of fence are used to enclose a rectangular pen, the resulting area of the pen is A=150x-x^2, where x is the width of the pen.

    a.What should the width be in order to have the max area?

    b.What is the maximum possible area?
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  2. #2
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    Quote Originally Posted by cdoubleokay View Post
    If 300 feet of fence are used to enclose a rectangular pen, the resulting area of the pen is A=150x-x^2, where x is the width of the pen.

    a.What should the width be in order to have the max area?

    b.What is the maximum possible area?
    Hello,

    to a.): You get the extreme value of A(x) if the first derivative of A equals zero.
    Calculate A'(x).
    Solve the equation A'(x) = 0 for x. (For confirmation only: x = 0 or x = 75)

    to b.): Plug in the result from a.) into the given equation of the function. Determine which of the 2 values is the maximum (for confirmation only: A_{max} = 5625)
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