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

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

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

extreme points

f (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)

p (x) = 12 x^{4} - 27 x^{3} + a x^{2} + 27 x - 6

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

f (x, y) = 8 + 76 x y + 38 x^{2} + 240 y + \frac{y ^{4}}{4}

y = \frac{x ^{2}}{ln ( x )}

f (x) = x^{3} - 6 x^{2} + 9 + 9, - 1 \leq x \leq 9

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