A value of c for which the conclusion of the Mean Value Theorem holds for the function f(x…

Question

A value of $c$ for which the conclusion of the Mean Value Theorem holds for the function $f(x)=\log_ex$ on the interval $[1,3]$ is

Accepted Answer

$f'(c)=\dfrac1c=\dfrac{f(3)-f(1)}{2}=\dfrac{\ln3}{2}\Rightarrow c=\dfrac{2}{\ln3}=2\log_3e$.

Solutions · 1