Determine whether the following statements are true and give an explanation or counterexample.

a. If the function f is differentiable for all values of x, then f is continuous for all values of x.

b. The function f(x) = |x + 1| is continuous for all x, but not differentiable for all x.

c. It is possible for the domain of f to be (a, b) and the domain of f' to be [a, b].