Mark each statement True or False. Justify each answer. (a) A continuous function defined on a bounded interval assumes maximum and minimum values. (b) If f is continuous on [a, b], then there exists...

Mark each statement True or False. Justify each answer.

(a) A continuous function defined on a bounded interval assumes maximum and minimum values.

(b) If f is continuous on [a, b], then there exists a point c ∈ (a, b) such that f ′(c) = [ f (b) − f (a)]/(b − a).

(c) Suppose f is differentiable on (a, b). If c ∈ (a, b) and f ′(c) = 0, then f (c) is either the maximum or the minimum of f on (a, b).