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

The extreme f(x,y)=xy-1/x-1/y is 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)=xy-1/x-1/y

extreme points

f (x, y) = x y - \frac{1}{x} - \frac{1}{y}

Minimum (- 1, - 1)

Solution steps

Find the critical points:

(- 1, - 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{2}{y ^{3}}

D (x, y) = \frac{4}{x ^{3} y ^{3}} - 1

Check the sign of at each critical point

Check critical point

(- 1, - 1) :

Minimum

Minimum (- 1, - 1)

What is the extreme f(x,y)=xy-1/x-1/y ?
The extreme f(x,y)=xy-1/x-1/y is Minimum(-1,-1)