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

a. The function f (x) = √x has a local maximum on the interval [0, ∞].

b. If a function has an absolute maximum on a closed interval, then the function must be continuous on that interval.

c. A function f has the property that f'(2) = 0. Therefore, f has a local extreme value at x = 2.

d. Absolute extreme values of a function on a closed interval always occur at a critical point or an endpoint of the interval.