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

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

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

extreme points

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

Saddle (- 1, - 3)

Solution steps

Find the critical points:

(- 1, - 3)

\frac{\partial ^{2} f}{\partial x ^{2}} = 0

D (x, y) = - 1

Check the sign of at each critical point

Check critical point

(- 1, - 3) :

Saddle

Saddle (- 1, - 3)

f (x) = 4 x^{2} - 32 ln (x)

y = - 6 - z^{2} - x^{2}

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

f (x) = - \frac{2}{3} x^{3} + 2 x^{2} + 6 x - 50

f (x) = x^{5} - 20 x^{4} + 8, 0 \leq x \leq 17

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