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

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

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

extreme points

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

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = - 5

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = 2 x^{2} - 4 x + 1

f (x) = x y - x - y

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

f (x) = x^{3} + 5

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

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