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

The extreme f(x,y)=x^2-y^2-xy+4x-2y is Saddle(-2,0)

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

extreme points

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

Saddle (- 2, 0)

Solution steps

Find the critical points:

(- 2, 0)

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

D (x, y) = - 5

Check the sign of at each critical point

Check critical point

(- 2, 0) :

Saddle

Saddle (- 2, 0)

f (x) = 2 x^{3} + 3 x^{2} - 72 x + 4, - 4 \leq x \leq 6

2 x

f (x) = \frac{x - 3}{x ^{2} - 9}

f (x, y) = 3 x^{3} - 12 x + 2 y^{2} - 8 y + 7

f (x, y) = (\frac{1}{16 - x ^{2} - y ^{2}})

What is the extreme f(x,y)=x^2-y^2-xy+4x-2y ?
The extreme f(x,y)=x^2-y^2-xy+4x-2y is Saddle(-2,0)