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 points

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

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)

f (x) = x^{2} - 9, - 3 \leq x \leq 4

y = \frac{x}{x ^{2} - x + 1}

f (x) = 4 x^{3} - 12 x^{2} + 8 x

f (x, y) = \frac{16 - x ^{2} - 4 y ^{2}}{2}

f (x) = (x + 3)^{2}

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…)