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). [Hint: Only uniqueness is in question.]
b. Show that Theorem 2.3 may not hold if inequality |g' (x)| ≤ k is replaced by g' (x) ≤ k. [Hint: Show that g(x) = 1 − x2, for x in [0, 1], provides a counterexample.]
Reference: Theorem 2.3
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