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

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

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

extreme points

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

Saddle (- 2, 2)

Solution steps

Find the critical points:

(- 2, 2)

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

D (x, y) = - 1

Check the sign of at each critical point

Check critical point

(- 2, 2) :

Saddle

Saddle (- 2, 2)

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

f (x) = x^{4} - 5 x^{3} + 9 x^{2}

f (x, y) = x y - 2 x - y + 6

f (x) = - (x - 1)^{2}

f (x) = \frac{( - 2 x ^{2} + 5 x - 1 )}{2 x - 1}

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