What is the extreme S(X,Y)=XY ?

The extreme S(X,Y)=XY is Saddle(0,0)

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extreme S(X,Y)=XY

extreme points

S (X, Y) = X Y

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (X, Y) = - 1

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = 2 x^{3} - 36 x^{2} + 162 x - 4

f (x) = 20 x (1 - x)^{3}

4 x^{3} - 48 x - 1

f (x) = x^{3} - 9 x^{2} + 15 x + 8

f (x, y) = 2 ln (x) + 4 ln (y) - 4 x^{2} - y