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

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

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

extreme points

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

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

Solution steps

Find the critical points:

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

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

D (x, y) = - 4 x^{2} + 4 x - 1

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(1, - 2) :

Saddle

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

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

g (x, y) = \frac{x ^{2} + y}{x ^{2} + y ^{2} + 1}

f (x) = - 2 x^{3} + 24 x^{2} - 42 x + 9

y = 9 x^{3} - 7 x^{2} + 3 x + 10

x^{2} - 1 + 2

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