If f: R to R is a differentiable function, x_0 is a point in R such that f'(x_0) = 0, and f''(x_0) > 0 (so in particular f'' exists at x_0), then there is a d > 0 so that f(x_0) < f(x) for all x in (x_0 - d, x_0 + d) that aren't equal to x_0.

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