5.

(a) If ¢ is continuous on a closed nondegenerate interval [a, b], differentiable on

(a, b), and ¢' is bounded on

(a, b), prove that ¢ is of bounded variation on

[a,b].

(b) Show that ¢(x) = ?Ix is of bounded variation on [-1,1] but ¢' is unbounded at some point in (-1,1).