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

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)

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)