Q. A 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
A) $2\log_{3}e$
B) $\frac{1}{2}\log_{e}3$
C) $\log_{3}e$
D) $\log_{e}3$
Explanation
(a)
Using Mean value theorem,
$f^{'}(c) = \frac{f(3) - f(1)}{3 - 1}$
$\Rightarrow \frac{1}{c} = \frac{\log_{e}{3 - \log_{e}1}}{1}$
$\Rightarrow c = \frac{2}{\log_{e}3} = 2\log_{3}e$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.