Racetrack Principle
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 Franky 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 f''(x) g''(x) for all x 0, and if f(0) = g(0), then f(x) g(x) for all x 0.…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 Franky 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 f''(x) g''(x) for all x 0, and if f(0) = g(0), then f(x) g(x) for all x 0.