What is the extreme f(x,y)=x^2-2y^2-5x-4y+xy ?

The extreme f(x,y)=x^2-2y^2-5x-4y+xy is Saddle(8/3 ,-1/3)

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extreme f(x,y)=x^2-2y^2-5x-4y+xy

extreme

Saddle (\frac{8}{3}, - \frac{1}{3})

Solution steps

Find the critical points:

(\frac{8}{3}, - \frac{1}{3})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 4

D (x, y) = - 9

Check the sign of at each critical point

Check critical point

(\frac{8}{3}, - \frac{1}{3}) :

Saddle

Saddle (\frac{8}{3}, - \frac{1}{3})

What is the extreme f(x,y)=x^2-2y^2-5x-4y+xy ?
The extreme f(x,y)=x^2-2y^2-5x-4y+xy is Saddle(8/3 ,-1/3)