What is the extreme x^2-2xy+3y^2-12y ?

The extreme x^2-2xy+3y^2-12y is Minimum(3,3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme x^2-2xy+3y^2-12y

extreme points

x^{2} - 2 x y + 3 y^{2} - 12 y

Minimum (3, 3)

Solution steps

Find the critical points:

(3, 3)

\frac{\partial ^{2} f}{\partial x ^{2}} = 6

D (x, y) = 8

Check the sign of at each critical point

Check critical point

(3, 3) :

Minimum

Minimum (3, 3)

f (x) = 2 x^{3} + 4 x^{2} + \frac{2}{1} x

f (x) = 2 x + \frac{32}{x}, x \neq = 0

f (\frac{24}{13}, \frac{88}{39}) = 3 x y - 4 x^{2} - 3 y^{2} + 8 x + 8 y - 4

- x^{3} + 75 x + 80

f (x) = x^{3} + 6 x^{2} + 5

What is the extreme x^2-2xy+3y^2-12y ?
The extreme x^2-2xy+3y^2-12y is Minimum(3,3)