Question: Let f : R R be a function which is twice continuously differentiable, i.e. f exists and is continuous. Suppose a R is a point

Let f : R R be a function which is twice continuously differentiable, i.e. f exists and is continuous. Suppose a R is a point with f (a) = 0 and f (a) > 0. Prove that there exists > 0 such that 0 < |x a| < = f(x) > f(a).

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