What is the extreme f(x,y)= 1/2 x^2+y^3-xy ?

The extreme f(x,y)= 1/2 x^2+y^3-xy is Minimum(1/3 , 1/3),Saddle(0,0)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x,y)= 1/2 x^2+y^3-xy

extreme

Minimum (\frac{1}{3}, \frac{1}{3}), Saddle (0, 0)

Solution steps

Find the critical points:

(\frac{1}{3}, \frac{1}{3}), (0, 0)

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

D (x, y) = 6 y - 1

Check the sign of at each critical point

Check critical point

(\frac{1}{3}, \frac{1}{3}) :

Minimum

Check critical point

(0, 0) :

Saddle

Minimum (\frac{1}{3}, \frac{1}{3}), Saddle (0, 0)

What is the extreme f(x,y)= 1/2 x^2+y^3-xy ?
The extreme f(x,y)= 1/2 x^2+y^3-xy is Minimum(1/3 , 1/3),Saddle(0,0)