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Math Help - Extreme Value problem

  1. #1
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    Extreme Value problem

    Hi I am having a bit of a struggle with this questions:

    A rectangle is inscribed in a semicircle of radius 2 cm. Find the largest area of such a rectangle.
    I have tried using sine and cosine but it is not working out. Any help would be appreciated.
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  2. #2
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    Try graphing it in the x and y plane, to get a semicircle with radius 2, and for the base you can use 2x and for the height use y.
    Note that this is an alternate for, using sin and cos should give you an answer, but since they don't ask for angles you are better off doing it like I said.
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  3. #3
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    Quote Originally Posted by NDHS View Post
    Hi I am having a bit of a struggle with this questions:

    A rectangle is inscribed in a semicircle of radius 2 cm. Find the largest area of such a rectangle.

    I have tried using sine and cosine but it is not working out. Any help would be appreciated.
    A = 2x\sqrt{4-x^2}

    find \frac{dA}{dx} and maximize.
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