A function is continuous on the closed interval and differentiable on
MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation
Problem
A function p is continuous on the closed interval [−1,4] and differentiable on (−1,4). Which statement best explains why p attains both an absolute maximum value and an absolute minimum value on [−1,4]?
(a) Because p is continuous on (−1,4).
(b) Because p has at least one critical number in (−1,4).
(c) Because the interval is closed and p is continuous on it.
(d) Because p is differentiable everywhere on [−1,4].