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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.

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Solution Summary

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

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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
...

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