What is the extreme f(x,y)=2x^3+3x^3y^2-4x^2y^2-2y ?

The extreme f(x,y)=2x^3+3x^3y^2-4x^2y^2-2y is Saddle(0.61561…,-1.22548…)

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extreme f(x,y)=2x^3+3x^3y^2-4x^2y^2-2y

extreme

Saddle (0.61561 \dots, - 1.22548 \dots)

Solution steps

Find the critical points:

(0.61561 \dots, - 1.22548 \dots)

\frac{\partial ^{2} f}{\partial x ^{2}} = 6 x^{3} - 8 x^{2}

D (x, y) = - 216 x^{4} y^{2} + 72 x^{4} + 384 x^{3} y^{2} - 96 x^{3} - 192 x^{2} y^{2}

Check the sign of at each critical point

Check critical point

(0.61561 \dots, - 1.22548 \dots) :

Saddle

Saddle (0.61561 \dots, - 1.22548 \dots)

What is the extreme f(x,y)=2x^3+3x^3y^2-4x^2y^2-2y ?
The extreme f(x,y)=2x^3+3x^3y^2-4x^2y^2-2y is Saddle(0.61561…,-1.22548…)