What is the extreme f(x,y)=xy(30-x-y) ?

The extreme f(x,y)=xy(30-x-y) is Saddle(0,30),Maximum(10,10)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x,y)=xy(30-x-y)

extreme

Saddle (0, 30), Maximum (10, 10)

Solution steps

Find the critical points:

(0, 30), (10, 10)

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

D (x, y) = - 4 x y + 120 x - 4 x^{2} + 120 y - 4 y^{2} - 900

Check the sign of at each critical point

Check critical point

(0, 30) :

Saddle

Check critical point

(10, 10) :

Maximum

Saddle (0, 30), Maximum (10, 10)

What is the extreme f(x,y)=xy(30-x-y) ?
The extreme f(x,y)=xy(30-x-y) is Saddle(0,30),Maximum(10,10)