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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
Find the interval in which $f(x)=\log (1+x)-\frac{x}{1+x}$ is increasing.
  • ✓
    $(0, \infty)$
  • B
    $(-\infty, 0)$
  • C
    $(-\infty, 3)$
  • D
    None of these
✓

Answer

Correct option: A.
$(0, \infty)$
(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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