Apentix/AP Calculus AB/Unit 5: Analytical Applications of Differentiation/Question
AP Calculus ABmediummcq1 pt

Which statement must be true for a function ff that is continuous on [a,b][a,b]?

A.ff attains its absolute maximum only at a point where f′(x)=0f'(x)=0.
B.ff attains both an absolute maximum and an absolute minimum on [a,b][a,b].
C.If ff has a local maximum at an interior point cc, then f(c)f(c) is the absolute maximum of ff on [a,b][a,b].
D.ff is differentiable on (a,b)(a,b).

Explanation

Core Concept

This is the Extreme Value Theorem. A function continuous on a closed interval attains both an absolute maximum and an absolute minimum there.

Correct Answer

Bff attains both an absolute maximum and an absolute minimum on [a,b][a,b].

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