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) = 3 x + y - 6

\frac{( e ^{- x} )}{x - 5} + 1

f (x) = x e^{- 3 x}, 0 \leq x \leq 2

f (x) = \frac{x}{x ^{2} + 1} [- 1.2]

\frac{( x ^{2} - 1 )}{( x - 3 ) 6}

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)