The maximum value of $f(x) = \frac{\ln x}{x}$ for $x > 0$ is:
Step-by-Step Solution
Key Concept: Differentiate $f(x) = \frac{\ln x}{x}$ using the quotient rule, set $f'(x) = 0$, and confirm using the sign change (or $f''$) that this critical point is a maximum.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)