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

The extreme f(x,y)=x^3+x^2y+x-y is Saddle(-1,2),Saddle(1,-2)

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

extreme points

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

Saddle (- 1, 2), Saddle (1, - 2)

Solution steps

Find the critical points:

(- 1, 2), (1, - 2)

\frac{\partial ^{2} f}{\partial x ^{2}} = 0

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

Check the sign of at each critical point

Check critical point

(- 1, 2) :

Saddle

Check critical point

(1, - 2) :

Saddle

Saddle (- 1, 2), Saddle (1, - 2)

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

\frac{x ^{2} - 4}{x ^{2} + 4}

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

f (x, y) = 2 x^{3} + x y^{2} + 5 x^{2} + y^{2}

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

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