Question

Applying mean value theorem on $f\left(x\right)=\log x;x\in [1,e]$, the value of $c$ is

• A. $\log (e-1)$
• B. $e-1$
• C. $1-e$
• D. $2$

Answer 1

The correct option is B $e-1$

By applying LMVT on $[1,e]$, we get
$f^{\prime }\left(c\right)=\frac{f\left(e\right)-f\left(1\right)}{e-1}$
$\Rightarrow \frac{1}{c}=\frac{\log e-\log 1}{e-1}$
$\Rightarrow c=\frac{e-1}{1-0}=e-1$