To prove someone had been speeding even though the speed of their vehicle
when passing the check points was less than the speed limit. Since if the
average speed between the check points d/t (where d is the distance
between the check points and t the difference in the times of passing the
check points) is greater than the speed limit then by the mean value theorem
the vehicles instantaneous speed was greater than the speed limit at some
point between the check points.
RonL