Schritt 1: lokale Extremstellen
\(Grad(f) = (f_x,f_y) \, = \, \left\{ -3 \; x^{2} \; y + y^{2} + 3 \; y, -x^{3} + 2 \; x \; y + 3 \; x \right\}\)
Löse das GLS
\( \left\{ \left\{ x = 0, y = 0 \right\} , \left\{ x = \sqrt{3}, y = 0 \right\} , \left\{ x = -\sqrt{3}, y = 0 \right\} , \left\{ x = 0, y = -3 \right\} , \left\{ x = \frac{\sqrt{15}}{5}, y = -\frac{6}{5} \right\} , \left\{ x = -\frac{\sqrt{15}}{5}, y = -\frac{6}{5} \right\} \right\} \)
Schritt 2: Hesse Matrix bestimmen
\(H_f\left(x,y\right)=\left(\begin{matrix}f_{xx}\\f_{xy}\end{matrix}\begin{matrix}f_{yx}\\f_{yy}\end{matrix}\right) \)
Min: H positiv definit
Max: H negativ definit
Sattel: H indefinit
