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Application of Derivatives — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSApplication of Derivatives1 Mark
Question
The function $f(x)=\cot ^{-1} x+x$ increases in the interval
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Answer

(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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