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

The extreme f(x,y)=x^2-y^2+xy-x-y is Saddle(3/5 ,-1/5)

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

extreme points

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

Saddle (\frac{3}{5}, - \frac{1}{5})

Solution steps

Find the critical points:

(\frac{3}{5}, - \frac{1}{5})

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

D (x, y) = - 5

Check the sign of at each critical point

Check critical point

(\frac{3}{5}, - \frac{1}{5}) :

Saddle

Saddle (\frac{3}{5}, - \frac{1}{5})

f (x, y) = 2 x^{2} + y^{2} + 6 x y + 10 x - 6 y + 5

f (x, y) = 2 y^{3} - 3 y^{2} - 12 y + 2 x^{2} - 6 x + 3

f (x) = 2 x^{4} - 4 x^{2} + 6

f (x) = x e^{7 x^{2}}

f (x, y) = 5 x + 3 y + 2

What is the extreme f(x,y)=x^2-y^2+xy-x-y ?
The extreme f(x,y)=x^2-y^2+xy-x-y is Saddle(3/5 ,-1/5)