Let f : R → R be a differentiable and periodic function with period T. (i) Show that there is c ∈ (0, T) such that f′(c) = 0. (ii) Prove that f′ is periodic with period T. (iii) Assume that f is twice differentiable. Show that there is ξ ∈ (0, T) such that f′′(ξ) = 0 (there is an inflexion point)

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