Find the interval in which f(x)= (1+x)-x 1+x is increasing. - Vidyadip

Question

Find the interval in which $f(x)=\log (1+x)-\frac{x}{1+x}$ is increasing.

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Answer

(a) : Here, $f^{\prime}(x)=\frac{x}{(1+x)^2}$
So, critical point is $x=0$ only.
and disjoint intervals are $(-\infty, 0)$ and $(0, \infty)$.
So, $f(x)$ is increasing in $(0, \infty)$ and decreasing in $(-\infty, 0)$.

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