What is the extreme f(x,y)=4x^2+2y^2-2xy-10y-2x ?

The extreme f(x,y)=4x^2+2y^2-2xy-10y-2x is Minimum(1,3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x,y)=4x^2+2y^2-2xy-10y-2x

extreme points

f (x, y) = 4 x^{2} + 2 y^{2} - 2 x y - 10 y - 2 x

Minimum (1, 3)

Solution steps

Find the critical points:

(1, 3)

\frac{\partial ^{2} f}{\partial x ^{2}} = 4

D (x, y) = 28

Check the sign of at each critical point

Check critical point

(1, 3) :

Minimum

Minimum (1, 3)

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

f (x) = cos^{2} (x) - 2 sin (x)

f (x) = \frac{x}{x ^{2} + 1}, 0 \leq x \leq 2

f (x) = \frac{x ^{3}}{3} - 2 x^{2} - 12 x

10 x y

What is the extreme f(x,y)=4x^2+2y^2-2xy-10y-2x ?
The extreme f(x,y)=4x^2+2y^2-2xy-10y-2x is Minimum(1,3)