> But I'm not sure the policeman who ticketed you can prove it in front of the judge :-)
He just uses Rolle's theorem.
Believe it or not, way back in college calculus class (mid-1970s, which dates me), we actually
had a movie in class about this -- a state trooper ticketing a guy for speeding between toll
stations because of the too-high average speed, and then the cop goes on to explain Rolle's
theorum.
Hokey, yeah, but I still remember it. (That and the one in biology class where a
football-field full of students act out DNA transcription. Weird.)