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

The extreme f(x,y)=x^2-2x+y^2+2y+1 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)=x^2-2x+y^2+2y+1

extreme points

f (x, y) = x^{2} - 2 x + y^{2} + 2 y + 1

Minimum (1, - 1)

Solution steps

Find the critical points:

(1, - 1)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(1, - 1) :

Minimum

Minimum (1, - 1)

What is the extreme f(x,y)=x^2-2x+y^2+2y+1 ?
The extreme f(x,y)=x^2-2x+y^2+2y+1 is Minimum(1,-1)