What is the extreme f(x,y)=-2x^2-y^2+xy+8x+3y ?

The extreme f(x,y)=-2x^2-y^2+xy+8x+3y is Maximum(19/7 , 20/7)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x,y)=-2x^2-y^2+xy+8x+3y

extreme points

f (x, y) = - 2 x^{2} - y^{2} + x y + 8 x + 3 y

Maximum (\frac{19}{7}, \frac{20}{7})

Solution steps

Find the critical points:

(\frac{19}{7}, \frac{20}{7})

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

D (x, y) = 7

Check the sign of at each critical point

Check critical point

(\frac{19}{7}, \frac{20}{7}) :

Maximum

Maximum (\frac{19}{7}, \frac{20}{7})

f (x) = x^{4} - 3 x^{2} + x

f (x) = x^{3} - 12 x^{2} + 45 x + 3

f (x, y) = 1 + 2 x^{2} + 2 y^{2}

(x^{2} - 7 x) (y^{2} - 5 y)

f (x) = x^{2} + 2 x - 15

What is the extreme f(x,y)=-2x^2-y^2+xy+8x+3y ?
The extreme f(x,y)=-2x^2-y^2+xy+8x+3y is Maximum(19/7 , 20/7)