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

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

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

extreme points

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

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) = 9 x^{3} - 54 x^{2} + 81 x + 13

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

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

y^{3} + x^{3} - \frac{21}{2} y^{2} - 3 x + 30 y

f (x) = e^{8 x} + e^{- x}

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