What is the extreme x^2+xy+y^2-19y+120 ?

The extreme x^2+xy+y^2-19y+120 is Minimum(-19/3 , 38/3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme x^2+xy+y^2-19y+120

extreme points

x^{2} + x y + y^{2} - 19 y + 120

Minimum (- \frac{19}{3}, \frac{38}{3})

Solution steps

Find the critical points:

(- \frac{19}{3}, \frac{38}{3})

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(- \frac{19}{3}, \frac{38}{3}) :

Minimum

Minimum (- \frac{19}{3}, \frac{38}{3})

g (t) = 8 t - t^{4}, - 2 \leq t \leq 1

f (x) = - 0.03 x^{2} + 380 x - 100000

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

f (x) = x y - x - 2

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

What is the extreme x^2+xy+y^2-19y+120 ?
The extreme x^2+xy+y^2-19y+120 is Minimum(-19/3 , 38/3)