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

The extreme f(x,y)=x^2-y^2-x-y is Saddle(1/2 ,-1/2)

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

extreme points

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

Saddle (\frac{1}{2}, - \frac{1}{2})

Solution steps

Find the critical points:

(\frac{1}{2}, - \frac{1}{2})

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

D (x, y) = - 4

Check the sign of at each critical point

Check critical point

(\frac{1}{2}, - \frac{1}{2}) :

Saddle

Saddle (\frac{1}{2}, - \frac{1}{2})

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