Rolle's theorem might be used as a predictor in various cases(like where the spped in a given curve was maximum without differenciation);also for analysing graphs of a company's yearly performance,it can be used. Or else, it can just be used a mathematical tool in solving other problems.
A trucker travels 163 miles on a toll road with a speed limit of 70 miles per hour. The trucker completes the 163 mile journey in 2 hours. ... Then at least once in time while on the toll road, the trucker was going 81.5 miles per hour, well over the speed limit.