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Math Help - Use Lagrange multipliers to find the maximum and minimum

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    Use Lagrange multipliers to find the maximum and minimum

    Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. (If a value does not exist, enter NONE.)
    f(x,y,z) = 3x y 3z;
    x + y z = 0,
    x^2 + 2z^2 = 1
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    Quote Originally Posted by sammygirl2791 View Post
    Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. (If a value does not exist, enter NONE.)
    f(x,y,z) = 3x y 3z;
    x + y z = 0,
    x^2 + 2z^2 - 1

    find \nabla h = 0

    where h(x,y,z,\lambda_1 , \lambda_2) = 3x - y - 3z +\lambda_1 (x + y - z)+\lambda_2 (x^2 + 2z^2 - 1)
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    I can' figure out how to find y
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    Quote Originally Posted by sammygirl2791 View Post
    I can' figure out how to find y
    Show me your workings thus far.
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    Quote Originally Posted by sammygirl2791 View Post
    I can' figure out how to find y
    It is true that y does not appear in the gradient. However, after you have found, say, z as a function of x, you still have the two constraints, x+ y- z= 0 and [tex]x^2+ 2z^2= 1.

    The second allows you to solve for specific values of x and z. Put those into x+ y- z= 0 to find y.
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