Practicing Success
Practicing Success
CUET Preparation Today
The interval in which $f(x)=\cot^{-1} x+ x$ increases is |
$(-∞,∞)$ $(∞,−∞)$ $(0,∞)$ $(-∞,0)$ |
$(-∞,∞)$ |
Given, $f(x)=\cot^{-1} x+ x$, Differentiating both sides we get, $f'(x)=\frac{-1}{1+x^2}+1$ or $f'(x)=\frac{-1+1+x^2}{1+x^2}$ or $f'(x)=\frac{x^2}{1+x^2}$ Clearly, $f'(x)>0$ for all x. So, $f(x)$ increasing in $(-∞,∞)$ |
