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)

y = u (t - 1) - u (t - 4)

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

f (t) = x

f (x) = 4 x^{3} + 21 x^{2} - 294 x + 9

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)