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

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

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

extreme points

f (x, y) = 3 x^{2} + 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) = \frac{x ^{5}}{20} - 4 x^{3}

x^{3} + 9 x^{2}

f (x) = x^{3} + y^{3} - 27 x y

- \frac{6}{x - 7}

f (x, y) = (x - y) (x y - 1)

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