If an object moves in a straight line with position function s = f(t), then the average velocity between t = a and t = b is

f(b) - f(a)/b - a

and the velocity at t = c is f '(c). thus the mean value theorem tells us that at some time t = c between a and b the instantaneous velocity f '(c) is equal to the average velocity. for instance, if a car traveled 1600 km in 20 hours, then the speedometer must have read km/h at least once.

in general, the mean value theorem can be interpreted as saying that there is a number at which the instantaneous rate of change is equal to the average rate of change over an interval.