Mark each statement True or False. Justify each answer. (a) Suppose f and g are continuous on [a, b ] and differentiable on (a, b). If f ′(x) = g ′(x) for all x ∈ (a, b), then f and g differ by a...

Mark each statement True or False. Justify each answer.

(a) Suppose f and g are continuous on [a, b ] and differentiable on (a, b). If f ′(x) = g ′(x) for all x ∈ (a, b), then f and g differ by a constant.

(b) If f is differentiable on (a, b) and c ∈ (a, b), then f ′ is continuous at c.

(c) Suppose f is differentiable on an interval I. If f is not injective on I, then there exists a point c ∈ I such that f ′(c) = 0.