Chapter 5.5, Problem 67E

The mean value theorem states that if F(x) is a differentiable function on the interval [a, b], then there exists some number c between a and b such that

     $F^{\prime }\left(c\right)=\frac{F\left(b\right)-F\left(a\right)}{b-a}$

Explain why the mean value theorem implies that if a car averages 60 miles per hour in some 10-minute interval, then the car’s instantaneous velocity is 60 miles per hour at least once in that interval.