The value of $c$ for which the conclusion of mean value theorem-holds for the function $f(x)=\log _e x$ on the interval $[1,3]$, is
Answer & explanation
Correct answer: option 1
Using Mean Value Theorem, we have
$f^{\prime}(c)=\frac{f(3)-f(1)}{3-1} \Rightarrow \frac{1}{c}=\frac{1}{2}\{\log 3-\log 1\} \Rightarrow c=2 \log _3 e$