For a function that is differentiable at

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

Problem

For a function ff that is differentiable at x=ax=a, which one of the following statements correctly describes the relationship between the average rate of change on [a,a+h][a,a+h] and the derivative f′(a)f'(a) as h→0h\to 0? (a) The average rate of change equals f′(a)f'(a) for every non-zero hh. (b) The average rate of change approaches 00 as h→0h\to 0. (c) The average rate of change approaches f′(a)f'(a) as h→0h\to 0. (d) The average rate of change becomes unbounded as h→0h\to 0.

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