a. Show that Theorem 2.2 is true if the inequality |g'(x)|≤k is replaced by g'(x) ≤ k, for all x∈(a,b).
b. Show that Theorem 2.3 may not hold if inequality |g'(x)| ≤ k is replaced by g'(x) ≤ k. [Show that g(x) = 1 − x2, for x in [0, 1], provides a counterexample.]