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

The extreme f(x,y)=2xy+x^2y-y is Saddle(-1+sqrt(2),0),Saddle(-1-sqrt(2),0)

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

extreme points

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

Saddle (- 1 + 2, 0), Saddle (- 1 - 2, 0)

Solution steps

Find the critical points:

(- 1 + 2, 0), (- 1 - 2, 0)

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

D (x, y) = - 4 x^{2} - 8 x - 4

Check the sign of at each critical point

Check critical point

(- 1 + 2, 0) :

Saddle

Check critical point

(- 1 - 2, 0) :

Saddle

Saddle (- 1 + 2, 0), Saddle (- 1 - 2, 0)

f (x) = 5 x^{\frac{2}{3}} - 2 x^{\frac{5}{3}}

f (x) = ln (x^{2} + x + 1)

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

V, V = 13 π r 2 h

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

What is the extreme f(x,y)=2xy+x^2y-y ?
The extreme f(x,y)=2xy+x^2y-y is Saddle(-1+sqrt(2),0),Saddle(-1-sqrt(2),0)