   Chapter 10.4, Problem 57E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Is the average rate of change of a function over [ a , b ] affectedby the values of the function between a and b? Explain.

To determine

Whether the average rate of change of a function over [a,b] is affected by the values of the function between a and b.

Explanation

Consider that a function is given over the interval [a,b].

Average rate of change of f over the interval [a,b] is given by the following formula:

Average rate of change of f=Change in fChange in x=ΔfΔx=f(b)f(a)ba

Consider the provided interval [2,5],

From the graph shown below, find the value of stock price function S(t) corresponding to interval [2,5]:

So,

S(2)=23, S(5)=27

As, the average rate of change of f(x) over the interval [a,b] is given by:

Average rate of change of f=f(b)f(a)b<

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