Which of the following best describes the average rate of change of a differentiable…

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

Problem

Which of the following best describes the average rate of change of a differentiable function

f

on the closed interval

[a,b]

with

a<b

? (a) It equals the instantaneous rate of change of

f

at the midpoint

x=\tfrac{a+b}{2}

. (b) It equals the slope of the secant line connecting the points

(a,f(a))

and

(b,f(b))

on the graph of

f

. (c) It equals the limit of

\dfrac{f(x)-f(a)}{x-a}

x

approaches

a

. (d) It equals the average of the instantaneous rates of change at the endpoints,

\dfrac{f'(a)+f'(b)}{2}

Related theory

Derivative Foundations

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