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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=x^2+xy+y^2-2x-y

extreme points

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

Minimum (1, 0)

Solution steps

Find the critical points:

(1, 0)

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(1, 0) :

Minimum

Minimum (1, 0)

f (x) = \frac{2 x ^{2}}{x - 2}, - 2 \leq x \leq 1

x^{3} - x^{2} - 8 x + 8

f (x, y) = 2 x y - 4 x - 3 y

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

f (x) = 4 x^{2} - 32 ln (x)

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