$$f(x) = f(x_0) + \fracdfdx(x_0)(x-x_0) + \frac12!\fracd^2fdx^2(x_0)(x-x_0)^2 + \ldots$$
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: Reformulating Newton's laws for complex, multi-particle systems. $$f(x) = f(x_0) + \fracdfdx(x_0)(x-x_0) + \frac12