What is the extreme f(x,y)=-5x^2-8y^2-2xy+42x+102y ?

The extreme f(x,y)=-5x^2-8y^2-2xy+42x+102y is Maximum(3,6)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x,y)=-5x^2-8y^2-2xy+42x+102y

extreme points

f (x, y) = - 5 x^{2} - 8 y^{2} - 2 x y + 42 x + 102 y

Maximum (3, 6)

Solution steps

Find the critical points:

(3, 6)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 16

D (x, y) = 156

Check the sign of at each critical point

Check critical point

(3, 6) :

Maximum

Maximum (3, 6)

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

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

f (x) = t^{3} - 15 t^{2} + 72 t + 8

f (x) = \frac{7}{12} x^{3} + 7 x^{2} + 21 x + 9

R (x, y) = - 5 x^{2} - 4 y^{2} - 4 x y + 68 x + 72 y

What is the extreme f(x,y)=-5x^2-8y^2-2xy+42x+102y ?
The extreme f(x,y)=-5x^2-8y^2-2xy+42x+102y is Maximum(3,6)