Question: Exercise 4.2.4. Let I R be an open interval, let c I and let f: I R be a function. Suppose that |f(x)| (x c)^2

Exercise 4.2.4. Let I R be an open interval, let c I and let f: I R be a function. Suppose that |f(x)| (x c)^2 for all x I. Prove that f is differentiable at c and f'(c) = 0. (The function f in Example 4.2.5 (1) is a special case of this exercise, where c = 0.)

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