Question

The maximum value of \(f(x)=\frac {\log (x)}{x}\) is 1/e at
1. x = 1
2. x = e
3. x = 1/e
4. None of these

Answer 1

Correct Answer - Option 2 : x = e

Explanation:

\(f(x)=\frac {\log (x)}{x}\)

For x = 1

\(f(1)=\frac {\log (1)}{1} = 0\)  [∵ log(1) = 0]

For x = e

\(f(e)=\frac {\log (e)}{e} = \frac 1 e\)   [∵ log(e) = 1]

For x = 1/e

\(f\left(\frac{1}{e}\right)=\frac {\log (\frac 1e)}{\frac 1e} \) = e [log (1) - log (e)] = e [0 - 1] = -e