Which of the following statements is ALWAYS true if exists for a real-valued function ?

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Which of the following statements is ALWAYS true if f′(a)f'(a) exists for a real-valued function ff? (a) f′(a)=0f'(a)=0. (b) ff has a local maximum at x=ax=a. (c) ff is continuous at x=ax=a. (d) ff is differentiable in some open interval containing aa.

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