Question

The function $f(x)=\cot ^{-1} x+x$ increases in the interval :

• A. $(1, \infty)$
• B. $(-1, \infty)$
• C. $(-\infty, \infty)$
• D. $(0, \infty)$

Answer 1

Answer: (C)

Key Idea : A function $f(x)$ is said to be increasing function, if $f^{\prime}(x)>0$
$\because f(x)=\cot ^{-1} x+x$
$\therefore f'(x)=-\frac{1}{1+x^{2}}+1=\frac{x^{2}}{1+x^{2}}$
Hence, $f(x)$ is increasing function since $f'(x)>0$ for all $x$