(a) Let f be differentiable on (a, b) and suppose that there exists m ∈ such that | f ′(x) | ≤ m for all x ∈ (a, b). Prove that f is uniformly continuous on (a, b). (b) Find an example of a function...

(a) Let f be differentiable on (a, b) and suppose that there exists m ∈

such that | f ′(x) | ≤ m for all x ∈ (a, b). Prove that f is uniformly continuous on (a, b).

(b) Find an example of a function f that is differentiable and uniformly continuous on (0, 1), but such that f ′ is unbounded on (0, 1).