Question: Find the critical points of \(f(x, y)=x^{2}-4 x y+y^{3}+4 y\) and classify them as local min, max, saddle points or none of these. Show your work. Recall \(D(a, b)=f_{x x} f_{y y}-\left(f_{x y}\right)^{2}\) evaluated at \((a, b)\) and that when \(\mathrm{D}<0\) there is a saddle point, \(\mathrm{D}>0\) there is a local max or \(\mathrm{min}\), and that when \(\mathrm{D}=0\) the test is inconclusive for the critical point \((a, b)\).

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