Maximum value of $\log x/x$ in interval $[2 , ∞]$ is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $1/e$
$f'(x)=\frac{1}{x^2}(1-\ln x)$
Clearly f(x) increasing for x < e and decreases for x > e
⇒ x = e is the point of local maxima
∴ maximum f(x) = $\frac{1}{e}$
Hence (3) is the correct answer.