A function f(x) has periodic derivative. In other words, f'(x +p) = f'(x) for some real value of p. Is f(x) necessarily periodic? Prove or give a counterexample.
I believe it is true simply because of trigonometric functions. However, I do not know how to prove it. I want to claim if the derivative is periodic than the anti-derivative is also periodic. However, I don't think that is good enough. Any hints?