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Math Help - Maxima And minima

  1. #1
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    Maxima And minima

    Please help me solve the following

    A farmer has 40 m of fencing with which to enclose a rectangle pen.
    Given the pen is x cm wide,

    a). show that the area is (20x -x^2)m^2
    b) Deduce the maximum area that he can enclose.
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  2. #2
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    Quote Originally Posted by mazy22a View Post
    Please help me solve the following

    A farmer has 40 m of fencing with which to enclose a rectangle pen.
    Given the pen is x cm wide,

    a). show that the area is (20x -x^2)m^2
    b) Deduce the maximum area that he can enclose.
    perimeter, P = 2(L+W)

    40 = 2(L + x)

    20 = L + x

    L = 20 - x

    A = LW

    A = (20 - x)x = 20x - x^2

    if you graph the area function, it will look like an inverted parabola. the maximum will be located at the parabola's vertex.

    Do you know how to find the x-value for the vertex of a parabola?
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  3. #3
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    thanks

    yeh maximum is 100 m^2

    worked it out by completing the square on

    - X^2 - 20x

    cheers mate
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