Concept explainers
a.
To find: the average rate of change of the linear function.
a.
Answer to Problem 22E
The average rate of change is
Explanation of Solution
Given information:
The linear function is
Formula used:
Calculation:
Substitution of
Therefore, the average rate of change is obtained as:
Hence, the average rate of change is
b.
To show: the average rate of change is the same as the slope of the line.
b.
Explanation of Solution
Given information:
The linear function is
Formula used:
Standard equation of line in Slope-intercept form is:
Proof:
Compare
Therefore, the slope of line is
Hence, the slope of line is
So, both the slope and average rate of change is same.
[PROVED]
Chapter 2 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning