What is the extreme f(x,y)=(9+xy)(x+y) ?

The extreme f(x,y)=(9+xy)(x+y) is Saddle(-3,3),Saddle(3,-3)

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extreme f(x,y)=(9+xy)(x+y)

extreme points

f (x, y) = (9 + x y) (x + y)

Saddle (- 3, 3), Saddle (3, - 3)

Solution steps

Find the critical points:

(- 3, 3), (3, - 3)

\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

(- 3, 3) :

Saddle

Check critical point

(3, - 3) :

Saddle

Saddle (- 3, 3), Saddle (3, - 3)

f (x) = 3 x^{5} - 5 x^{3} + 1

f (x) = x^{3} + 3 x^{2} - 9 x + 5

f (x) = 5 x^{3} + 2 x^{2} - 3 x

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

f (x) = \frac{- 12 x ^{3} + x}{x}

What is the extreme f(x,y)=(9+xy)(x+y) ?
The extreme f(x,y)=(9+xy)(x+y) is Saddle(-3,3),Saddle(3,-3)