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Thread: Calculus Problem

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  1. Dec 1st, 2001, 05:34 AM #4
    riis
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    Shaunak's right.
    I'll work it out some more.

    x = size of square bottom
    y = height

    8x + 4y = 100
    y = 25 - 2x

    Volume: x ^ 2 * y = x ^ 2 ( 25 - 2x) = 25x ^ 2 - 2x ^ 3
    Derivate of this should be 0 for extreme value.
    Derivate: 50x - 6x ^ 2 = 0 => 50 - 6x = 0 => x = 50 / 6 = 8 1/3

    Surface: 2x ^ 2 + 4xy = 2x ^ 2 + 100x - 8x ^ 2 = -6x ^ 2 + 100x
    Derivate: -12x + 100 = 0 => x = 100 / 12 = 8 1/3

    This (coincidally?) will result in a cube, which seems most logical.
    Last edited by riis; Dec 1st, 2001 at 05:44 AM.
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