Let f : ℝ → ℝ be a differentiable function such that f and its derivative f' have no common zeros in [0, 1]. Which one of the following statements Is true?
1
f never vanishes in [0, 1].
2
f has at most finitely many zeros in [0, 1].
3
f has infinitely many zeros in [0, 1].
4
f(1/2) = 0.