Precalculus: Mathematics for Calculus - 6th Edition

6th Edition

ISBN: 9780840068071

Author: Stewart, James, Redlin, Lothar, Watson, Saleem

Publisher: Cengage Learning

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Concept explainers

Exponential Growth Model

The relation that represents an exponential function is:

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Textbook Question

Chapter 2.4, Problem 4E

(a) The average rate of change of a function f between x = a and x = b is the slope of the __________ line between (a, f(a)) and (b, f(b)).
(b) The average rate of change of the linear function f(x) = 3x + 5 between any two points is _____.

(a)

Expert Solution

To determine

To fill: The average rate of change of function f between x=a and x=b is slope of which line between (a,f(a)) and (b,f(b)) .

Answer to Problem 4E

The average rate of change of a function is the slope of the secant line between (a,f(a)) and (b,f(b)) .

Explanation of Solution

Given:

Average rate of change of function y=f(x) between x=a and x=b .

Average rate of change =Change in yChange in x=f(b)−f(a)b−a

So, the average rate of change of a function is the slope of the secant line between (a,f(a)) and (b,f(b)) .

(b)

Expert Solution

To determine

To fill: The average rate of change of linear function f(x)=3x+5 between any two point.

Answer to Problem 4E

The average rate of change of linear function f(x)=3x+5 between any two point is 3.

Explanation of Solution

Formula used:

Average rate of change of function y=f(x) between x=a and x=b .

Average rate of change =Change in yChange in x=f(b)−f(a)b−a (1)

Given:

The given function is,

f(x)=3x+5 . (2)

Calculation:

Suppose the two point between which the average rate of change of the linear function is to be calculated is x=x1 and x=x2 .

Substitute x1 for a and x2 for b in equation (1)

Average rate of change=f(x1)−f(x2)x1−x2 (3)

For, f(x1) substitute x1 for x in equation (1)

f(x1)=3x1+5

For, f(x2) substitute x2 for x in equation (1)

f(x2)=3x2+5

Substitute 3x1+5 for f(x1) and 3x2+5 for f(x2) in equation (3), to calculate the average rate of change.

Average rate of change=3x1+5−(3x2+5)(x1−x2)=3(x1−x2)+5−5(x1−x2)=3(x1−x2)(x1−x2)=3

Therefore, the average rate of change of linear function f(x)=3x+5 between any two point is 3.

Chapter 2.4, Problem 3E

Chapter 2.4, Problem 5E

Chapter 2 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

Ch. 2.1 - Prob. 1E Ch. 2.1 - For a function f, the set of all possible inputs...Ch. 2.1 - (a) Which of the following functions have 5 in...Ch. 2.1 - A function is given algebraically by the formula...Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

Ch. 2.1 - Prob. 11E Ch. 2.1 - Prob. 12E Ch. 2.1 - Prob. 13E Ch. 2.1 - Prob. 14E Ch. 2.1 - Prob. 15E Ch. 2.1 - Prob. 16E Ch. 2.1 - Prob. 17E Ch. 2.1 - Prob. 18E Ch. 2.1 - Prob. 19E Ch. 2.1 - Prob. 20E Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.1 - Prob. 34E Ch. 2.1 - Prob. 35E Ch. 2.1 - Prob. 36E Ch. 2.1 - Prob. 37E Ch. 2.1 - Prob. 38E Ch. 2.1 - Prob. 39E Ch. 2.1 - Prob. 40E Ch. 2.1 - Prob. 41E Ch. 2.1 - Prob. 42E Ch. 2.1 - Prob. 43E Ch. 2.1 - Prob. 44E Ch. 2.1 - Prob. 45E Ch. 2.1 - Prob. 46E Ch. 2.1 - Prob. 47E Ch. 2.1 - Prob. 48E Ch. 2.1 - Prob. 49E Ch. 2.1 - Prob. 50E Ch. 2.1 - Prob. 51E Ch. 2.1 - Prob. 52E Ch. 2.1 - Prob. 53E Ch. 2.1 - Prob. 54E Ch. 2.1 - Prob. 55E Ch. 2.1 - Prob. 56E Ch. 2.1 - Prob. 57E Ch. 2.1 - Prob. 58E Ch. 2.1 - Prob. 59E Ch. 2.1 - Prob. 60E Ch. 2.1 - Prob. 61E Ch. 2.1 - Prob. 62E Ch. 2.1 - Prob. 63E Ch. 2.1 - Prob. 64E Ch. 2.1 - Prob. 65E Ch. 2.1 - Prob. 66E Ch. 2.1 - Prob. 67E Ch. 2.1 - Prob. 68E Ch. 2.1 - Prob. 69E Ch. 2.1 - Prob. 70E Ch. 2.1 - Prob. 71E Ch. 2.1 - Prob. 72E Ch. 2.1 - Prob. 73E Ch. 2.1 - Prob. 74E Ch. 2.1 - Relativity According to the Theory of Relativity,...Ch. 2.1 - Income Tax In a certain country, income tax T is...Ch. 2.1 - Internet Purchases An Internet bookstore charges...Ch. 2.1 - Cost of a Hotel Stay A hotel chain charges 75 each...Ch. 2.1 - Speeding Tickets In a certain state the maximum...Ch. 2.1 - Height of Grass A home owner mows the lawn every...Ch. 2.1 - Prob. 81E Ch. 2.1 - Prob. 82E Ch. 2.1 - Prob. 83E Ch. 2.1 - Prob. 84E Ch. 2.1 - Prob. 85E Ch. 2.2 - Prob. 1E Ch. 2.2 - Prob. 2E Ch. 2.2 - Prob. 3E Ch. 2.2 - Match the function with its graph. 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(a) The average rate of change of a function f between x = a and x = b is the slope of the ______ line between ( a , f ( a )) and ( b , f ( b )). (b) The average rate of change of the linear function f ( x ) = 3 x + 5 between any two points is _.

Solution Summary: The author explains the average rate of change of linear function f(x)=3x+5 between any two points.

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Answer to Problem 4E

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Answer to Problem 4E

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(a) The average rate of change of a function f between x = a and x = b is the slope of the __________ line between ( a , f ( a )) and ( b , f ( b )). (b) The average rate of change of the linear function f ( x ) = 3 x + 5 between any two points is _____.

Solution Summary: The author explains the average rate of change of linear function f(x)=3x+5 between any two points.

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Answer to Problem 4E

Explanation of Solution

Answer to Problem 4E

Explanation of Solution

Chapter 2 Solutions

(a) The average rate of change of a function f between x = a and x = b is the slope of the ______ line between ( a , f ( a )) and ( b , f ( b )). (b) The average rate of change of the linear function f ( x ) = 3 x + 5 between any two points is _.