Let ƒ be a function that is differentiable on [a, b] .  we defined the average rate of change of ƒ over [a, b] to be ƒ(b) - ƒ(a)/( b - a) and the instantaneous rate of change of ƒ at x to be ƒ′(x). In this chapter we defined the average value of a function. For the new definition of average to be consistent with the old one, we should have ƒ(b) - ƒ(a)/( b - a) = average value of ƒ′ on [a, b]. Is this the case? Give reasons for your answer.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 13SE: For the following exercises, find the average rate of change of each function on the interval...
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Let ƒ be a function that is differentiable on [a, b] .  we defined the average rate of change of ƒ over [a, b] to be

ƒ(b) - ƒ(a)/( b - a) and the instantaneous rate of change of ƒ at x to be ƒ′(x). In this chapter we defined the average value of a function. For the new definition of average to be consistent with the old one, we should have

ƒ(b) - ƒ(a)/( b - a) = average value of ƒ′ on [a, b].

Is this the case? Give reasons for your answer.

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