Question

The function $\frac{\log x}{x}$ is increasing in

• A. (1,2 e)
• B. (0, e)
• C. (2,2 e)
• D. (1 / e, 2 e)

Answer 1

Answer: (B)

Let $y=\frac{\log x}{x} $
$\Rightarrow \frac{d y}{d x}=\frac{x(1 / x)-\log x}{x^{2}} $
$=\frac{1-\log x}{x^{2}}$
$y$ is increasing if $\frac{1-\log x}{x^{2}}>0$
$\Rightarrow 1-\log x>0$
$\Rightarrow \log x< 1$
$\Rightarrow x< e$
$\therefore y$ is increasing in $(0, e)$.