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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
The function $f(x)=\cot ^{-1} x+x$ increases in the interval
  • A
    $(1, \infty)$
  • B
    $(-1, \infty)$
  • C
    $(0, \infty)$
  • ✓
    $(-\infty, \infty)$
✓

Answer

Correct option: D.
$(-\infty, \infty)$
(d) : $f(x)=\cot ^{-1} x+x$
$
\Rightarrow f^{\prime}(x)=\frac{-1}{1+x^2}+1 \Rightarrow f^{\prime}(x)=\frac{x^2}{1+x^2} \geq 0 \text {, for } x \in R
$
$\therefore f(x)$ is increasing on $(-\infty, \infty)$.

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