Question: Let I be an open interval which contains 0 and f : I R. If there exists an a > 1 such that |f(x)|

Let I be an open interval which contains 0 and f : I → R. If there exists an a > 1 such that |f(x)| < |x|a for all x ∊ I, prove that f is differentiable at 0. What happens when a = 1?

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