What is the extreme g(x,y)=x^2-3xy-y^2 ?

The extreme g(x,y)=x^2-3xy-y^2 is Saddle(0,0)

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extreme g(x,y)=x^2-3xy-y^2

extreme points

g (x, y) = x^{2} - 3 x y - y^{2}

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = - 13

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

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

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

f (x, y) = x^{4} + y^{4} - x y

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

f (x) = - 3 x^{4} + 8 x^{3} - 6 x^{2} - 2

What is the extreme g(x,y)=x^2-3xy-y^2 ?
The extreme g(x,y)=x^2-3xy-y^2 is Saddle(0,0)