Question

$f\left(x\right)=\frac{\log x}{x}(x>0)$ is increasing in

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

Answer 1

The correct option is A $(0,e)$

$f^{\prime }\left(x\right)=\frac{1}{x^2}-\frac{\log x}{x^2}$
$f^{\prime }\left(x\right)=0$ for $x=e$
$f^{\prime }\left(x\right)>0$ If $0<x<e$
$f^{\prime }\left(x\right)<0$ If $x>e$