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

The extreme f(x,y)=2x+y+2/x-(y^2)/2 is Saddle(1,1),Maximum(-1,1)

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+y+2/x-(y^2)/2

extreme points

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

Saddle (1, 1), Maximum (- 1, 1)

Solution steps

Find the critical points:

(1, 1), (- 1, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 1

D (x, y) = - \frac{4}{x ^{3}}

Check the sign of at each critical point

Check critical point

(1, 1) :

Saddle

Check critical point

(- 1, 1) :

Maximum

Saddle (1, 1), Maximum (- 1, 1)

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

f (x) = 3 x^{4} + 8 x^{3} - 6 x^{2} - 24 x

x^{3} - 3 x^{2} - 9 x + 1

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

f (x) = x^{2} - y^{2} - 2 x + 4 y + 6

What is the extreme f(x,y)=2x+y+2/x-(y^2)/2 ?
The extreme f(x,y)=2x+y+2/x-(y^2)/2 is Saddle(1,1),Maximum(-1,1)