Question

At $x=e$, the function $f\left(x\right)=\frac{\ln x}{x}$ is

• A. Increasing
• B. Decreasing
• C. Non monotonic
• D. Monotonic

Answer 1

The correct option is C Non monotonic

Given, $f\left(x\right)=\frac{\ln x}{x}$
$\Rightarrow f^{\prime }\left(x\right)=\frac{1-\ln x}{x^2}$
Now, $f^{\prime }\left(e\right)=0$
Also, $f^{\prime }\left(e^{-}\right)>0$ and $f^{\prime }\left(e^{+}\right)<0$
Hence $f\left(x\right)$ is non-monotonic at $x=e$