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Math Help - Lagrange Multiplier

  1. #1
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    Lagrange Multiplier

    See attach for the question. My answer is incorrect. Where did I go wrong?

    V = x^2y = 900

    SA = 6xy

    f_x = 6y

    f_y = 6x

    g_x = 2xy

    g_y = x^2

    6x = 2xy \lambda

    6x = x^2 \lambda

    \frac{3x}{xy} = \frac{6x}{x^2}

    3x^3 = 6x^2y

    \frac{1}{2}x = y

    x^2 (\frac{1}{2}x) = 900

    x = 12.1644

    y = 6.0822
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  2. #2
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    Quote Originally Posted by Macleef View Post
    See attach for the question. My answer is incorrect. Where did I go wrong?

    V = x^2y = 900

    SA = 6xy

    f_x = 6y

    f_y = 6x

    g_x = 2xy

    g_y = x^2

    6x = 2xy \lambda (**)

    6x = x^2 \lambda

    \frac{3x}{xy} = \frac{6x}{x^2}

    3x^3 = 6x^2y

    \frac{1}{2}x = y

    x^2 (\frac{1}{2}x) = 900

    x = 12.1644

    y = 6.0822
    I believe here (**)
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