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1. For the following functions, find all critical points, and classify whether they are local maximum, local minimum, or saddle points. (a) $f(x, y)=x^{2} y+\frac{4}{3} y^{3}-4 y$. (b) $f(x, y)=x^{3}+y^{3}+3 x^{2}-3 y^{2}-8$. (c) $f(x, y, z)=x^{3}+x y z+y^{2}-3 x$.

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