Let $f : \mathbb{R} → \mathbb{R}$ be a continuous function. Which of the following imply that it is uniformly continuous?
(a) $f$ is $2\pi$-periodic.
(b) $f$ is differentiable and its derivative is bounded on $\mathbb{R}$.
(c) $f$ is absolutely continuous.
my thoughts:
(a) is a periodic function so uniformly continuous.
(b) false.example $\sqrt[3]{x}$.here i am confused because the answer is given that it is also true.
(c) i am not sure.