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    What are the critical points of f(x, y) = x^3 + 6xy + 3y^2?

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    Find and classify the critical points in the function:

    f(x, y) = x^3 + 6xy + 3y^2.

    © BrainMass Inc. brainmass.com March 4, 2021, 5:50 pm ad1c9bdddf
    https://brainmass.com/math/critical-points-13918

    Solution Preview

    First we find the first partial derivatives:

    df/dx=3x^2+6y
    df/dy=6x+6y
    Note that df/dx and df/dy are actually the partial derivatives.

    Now we put these two terms equal to zero and solve for x and y.
    3x^2+6y=0 ---> y=-x^2/2
    6x+6y=0 ----> y=-x
    ...

    Solution Summary

    This solution shows how to find and classify critical points with step by step calculations and the answer.

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