What is the extreme (sqrt(x))/(1+x) ?

The extreme (sqrt(x))/(1+x) is Minimum(0,0),Maximum(1, 1/2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme (sqrt(x))/(1+x)

extreme points

\frac{x}{1 + x}

Minimum (0, 0), Maximum (1, \frac{1}{2})

Solution steps

f^{'} (x) = \frac{1 - x}{2 x ( 1 + x ) ^{2}}

Find intervals:

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = 0

into

\frac{x}{1 + x} : 0

Minimum (0, 0)

Plug

x = 1

into

\frac{x}{1 + x} : \frac{1}{2}

Maximum (1, \frac{1}{2})

Minimum (0, 0), Maximum (1, \frac{1}{2})

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

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

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

f (x) = \frac{- 8}{x ^{2} - 4}

f (x) = \frac{x ^{2} - x - 2}{x ^{2} - 6 x + 9}

What is the extreme (sqrt(x))/(1+x) ?
The extreme (sqrt(x))/(1+x) is Minimum(0,0),Maximum(1, 1/2)