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

The extreme f(x,y)=x^3+3xy-y^3 is Saddle(0,0),Minimum(1,-1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x,y)=x^3+3xy-y^3

extreme

Saddle (0, 0), Minimum (1, - 1)

Solution steps

Find the critical points:

(0, 0), (1, - 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 6 y

D (x, y) = - 36 x y - 9

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(1, - 1) :

Minimum

Saddle (0, 0), Minimum (1, - 1)

What is the extreme f(x,y)=x^3+3xy-y^3 ?
The extreme f(x,y)=x^3+3xy-y^3 is Saddle(0,0),Minimum(1,-1)