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    Lagrange multipliers

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    Use Lagrange multipliers to find maximum and minimum values of the function subject to a given constraint or constraints.

    1.)f(x,y,z)= xyz; x^2 + 2y^2 + 3z^2 = 6

    2.)f(x,y,z)= x^2 + y^2 + z^2; x^4 + y^4 + z^4 = 1

    3.)f(x,y,z)= x^4 + y^4 + z^4; x^2 + y^2 + z^2 = 1.

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    Solution Summary

    The solution provides an example of using Lagrange multipliers to find extreme values.