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, y) = 3 x - x^{3} - 2 y^{2} + y^{4}

f (x) = x^{4} - 2 x^{3} + x + 1

f (x) = 3 x^{3} + 16 x

f (x) = x - 2 sin (x)

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)