Question $4$

$10$ Points

Let $f(x,y)=\frac{4}{3}{y}^3-4xy+12y+\frac{x^2}{2}.$ Find the critical points of $f(x,y),$ and use the Hessian to classify each as a relative min, relative max, or saddle point.

Hint: the Hessian involves all four second partials..

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