Chapter 3.1, Problem 50E

Average Velocity Let $s\left(t\right)$ be the number of miles a car travels in $t$ hours. Then, the average velocity during the first $t$ hours is $\bar{v}\left(t\right)=s\left(t\right)/t$ miles per hour. If the average velocity is maximized at time $t_0$, show that at this time the average velocity $\bar{v}\left(t_0\right)$ equals the instantaneous velocity $s\text{'}\left(t_0\right)$. [Hint: Compute the derivative of $\bar{v}\left(t\right)$.]