AIEEE 2007 (Offline)Question 1
A value of $c$ for which the conclusion of Mean Value Theorem holds for the function $f(x)=\log_ex$ on the interval $[1,3]$ is
Differentiation and its Application
Solution
Concept. Set $f'(c)$ equal to the slope of the chord. Formulas used. (1) MVT: $f'(c)=\dfrac{f(3)-f(1)}{3-1}$Step 1 - Apply (1). $\dfrac1c=\dfrac{\ln3}{2}$. Step 2 - Solve. $c=\dfrac{2}{\ln3}=2\log_3e$ (about $1.82$, inside $(1,3)$). Answer: (C)