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

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

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

extreme points

f (x, y) = (1 + x y) (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) = 3 x^{4} - 4 x^{3} - 12 x^{2} + 1

f (x) = x^{3} - 3 x^{2} - 24 x + 2

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

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

f (x) = x^{4} - 2 x^{2} - 8

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