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 $y=\frac{\log x}{x}$
$\Rightarrow \frac{dy}{dx}=\frac{x(1/x)-\log x}{x^2}$
$=\frac{1-\log x}{x^2}$
$y$ 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 $(0,e)$.