Let s(t) be the number of miles a car travels in t hours. Then, the average velocity during the first t hours is v(t)=s(t)/t miles per hour.

Let s(t) be the number of miles a car travels in t hours. Then, the average velocity during the first t hours is v(t)=s(t)/t miles per hour. If the average velocity is maximized at time t0, show that at this time the average velocity v (t0) equals the instantaneous velocity s'(t0). [Hint: Compute the derivative of v(t).]