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

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

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

extreme points

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

Saddle (1, - 1)

Solution steps

Find the critical points:

(1, - 1)

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

D (x, y) = - 5

Check the sign of at each critical point

Check critical point

(1, - 1) :

Saddle

Saddle (1, - 1)

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

f (x) = 2 x^{3} - 3 x^{2} - 12

f (x) = x^{3} + 12 x^{2} - 27 x + 8 [- 10]

f (x) = \frac{- 5}{3 x ^{2} - 24 x + 50}

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

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