What is the extreme F(X,Y)=X(X+Y)+X(X+Y) ?

The extreme F(X,Y)=X(X+Y)+X(X+Y) is Saddle(0,0)

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extreme F(X,Y)=X(X+Y)+X(X+Y)

extreme points

F (X, Y) = X (X + Y) + X (X + Y)

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial X ^{2}} = 0

D (X, Y) = - 4

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

- x^{2} - 3.7 x - 6.5

f (x) = - 2 x^{3} + 33 x^{2} - 168 x + 10

f (x) = 4 x^{3} - 6 x^{2} - 144 x + 1

f (x, y) = \frac{20480}{x} + \frac{20480}{y} + 5 x y

f (x) = 2 x^{3} + 6 x^{2} - 144 x + 2, - 6 \leq x \leq 5

What is the extreme F(X,Y)=X(X+Y)+X(X+Y) ?
The extreme F(X,Y)=X(X+Y)+X(X+Y) is Saddle(0,0)