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

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

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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})

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