Assume that f : R → R is differentiable, that ƒ(0) = 1, ƒ(1) = 3 and ƒ(4) = −1. Which, if any, of the following statements necessarily follow? Choose all that apply. There exists c = (0, 1) such that f'(c) = 2 There exists c = (1, 4) such that ƒ (c) = 0 For all x € (0,1), f(x) > 0 f has at least one critical point f attains a maximum value None of these necessarily follow.

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