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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

extreme points

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

Minimum (1, 1)

Solution steps

Find the critical points:

(1, 1)

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(1, 1) :

Minimum

Minimum (1, 1)

f (x) = x^{2} + x y + y^{2} - 7 y + 16

f (x, y) = x^{2} + x y + y^{2} + 7 y

f (x) = \frac{7 ( x - 1 ) ^{2}}{x + 9}, (- 21, - 9)

\frac{7 x - 2}{3}

f (x) = x^{3} + y^{3} - 21 x y

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