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Find the intervals in which the function...

Find the intervals in which the function `f(x)=log(1+x)-(2x)/(2+x)` is increasing or decreasing.

A

` (0,oo)`

B

`(-oo, 0)`

C

`(-oo,oo)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `f(x)=log(1+x)-(2x)/(2+x)`
`thereforef'(x)=(1)/(1+x)-((2+x)*2-2x)/((2+x)^(2))`
`=(x^(2))/((1+x)(x+2)^(2))`
Clearly, `f'(x)gt0` for all `x gt0.`
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