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Math Help - urgent math help needed on max and min

  1. #1
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    urgent math help needed on max and min

    I have no clue how to do this problem. please help.

    A rectangle has one side on the x -axis and two vertices on the curve:
    4/(2+x^2)

    Find the vertices of the rectangle with maximum area.
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  2. #2
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    Quote Originally Posted by jojoferni244 View Post
    I have no clue how to do this problem. please help.

    A rectangle has one side on the x -axis and two vertices on the curve:
    4/(2+x^2)

    Find the vertices of the rectangle with maximum area.
    Let the rectangle be symmetric. It has vertices at (-a, 0) and (a, 0). Then the width of the rectangle is 2a and the height of the rectangle is \frac{4}{2 + a^2}.

    Then the area of the rectangle is A = 2a \left(\frac{4}{2 + a^2} \right) = \frac{8a}{2 + a^2}.

    Use calculus to find the value of a that maximises A.
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