Rolle’s Theorem is indeed a hallmark in differential and integral calculus, according to Nikolai Luzin, Russian Mathematician (1883–1950); “Rolle’s theorem underlies the theoretical development of differential and integral calculus”. And differential and integral calculus beyond doubt play a vital role in multifarious fields of our practical life; few are as under;
1) Rolle’s theorem helps a lot in finding the maximum height of the projectile trajectory.
2) It has played a vital role in bringing architectural perfection in the construction of elliptical domes that enhances the amplitude of light (electromagnetic) and sound waves.
3) A few weeks ago I got the chance to apply Rolle’s theorem in finding a particular day in a certain interval when the number of registered COVID-19 cases remains the same.
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.