What is the extreme f(x,y)=(x-y)(1-xy) ?

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

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

extreme points

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

Saddle (1, 1), Saddle (- 1, - 1)

Solution steps

Find the critical points:

(1, 1), (- 1, - 1)

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

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

Check the sign of at each critical point

Check critical point

(1, 1) :

Saddle

Check critical point

(- 1, - 1) :

Saddle

Saddle (1, 1), Saddle (- 1, - 1)

f (x) = 2 x^{2} - 4 x - 1

f (x) = 3 x^{4} + 16 x^{3} + 24 x^{2} + 32

\frac{x ^{2}}{x ^{2} + 3}

f (x) = 88 - \frac{1}{2} x - \frac{3200}{x}

f (x) = - 2 x^{2} - 24 x - 71

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