How do you cross a room when there's an infinite number of points to visit? (Gee, thanks Zeno).Īnd yet, we move.So there's an infinite number of points on a line? Yep.Infinity is a constant source of paradoxes ("headaches"): This result came over thousands of years of thinking, from Archimedes to Newton. Equations exist to convey ideas: understand the idea, not the grammar.ĭerivatives create a perfect model of change from an imperfect guess. Let's step away from the gnarly equation. ![]() That's pretty interesting, more than the typical "the derivative is the slope of a function" description. Knowing this, you can plot the past/present/future, find minimums/maximums, and therefore make better decisions. Like this magic newspaper, the derivative is a crystal ball that explains exactly how a pattern will change. You could even stop using the monkeys that pick random stocks for your portfolio. Well, you'd apply the changes one-by-one, plot out future prices, and buy low / sell high to build your empire. Let's say I gave you a magic newspaper that listed the daily stock market changes for the next few years (+1% Monday, -2% Tuesday.). ![]() Psst! The derivative is the heart of calculus, buried inside this definition: How do you wish the derivative was explained to you? Here's my take.
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