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

The extreme f(x,y)=3x-4y+x^2y-xy^3 is Saddle(-1,1),Saddle(2.63883…,-0.61182…)

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

extreme

Saddle (- 1, 1), Saddle (2.63883 \dots, - 0.61182 \dots)

Solution steps

Find the critical points:

(- 1, 1), (2.63883 \dots, - 0.61182 \dots)

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

D (x, y) = - 4 x^{2} - 9 y^{4}

Check the sign of at each critical point

Check critical point

(- 1, 1) :

Saddle

Check critical point

(2.63883 \dots, - 0.61182 \dots) :

Saddle

Saddle (- 1, 1), Saddle (2.63883 \dots, - 0.61182 \dots)

What is the extreme f(x,y)=3x-4y+x^2y-xy^3 ?
The extreme f(x,y)=3x-4y+x^2y-xy^3 is Saddle(-1,1),Saddle(2.63883…,-0.61182…)