About: Racetrack principle

In calculus, the racetrack principle describes the movement and growth of two functions in terms of their derivatives. This principle is derived from the fact that if a horse named Frank Fleetfeet always runs faster than a horse named Greg Gooseleg, then if Frank and Greg start a race from the same place and the same time, then Frank will win. More briefly, the horse that starts fast and stays fast wins. In symbols: if for all , and if , then for all . or, substituting ≥ for > produces the theorem if for all , and if , then for all . which can be proved in a similar way