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

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

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

extreme points

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

w^{4} - 55 w^{2} + 1600

f (x) = \frac{- x ^{2}}{x ^{2} - 4}

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

y = x^{2} - 8 x, - \infty \leq x \leq 8

f (x) = 28 x^{\frac{1}{2}} - x

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