Concept explainers
- (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)
To fill: The average rate of change of function f between
Answer to Problem 4E
The average rate of change of a function is the slope of the secant line between
Explanation of Solution
Given:
Average rate of change of function
So, the average rate of change of a function is the slope of the secant line between
(b)
To fill: The average rate of change of linear function
Answer to Problem 4E
The average rate of change of linear function
Explanation of Solution
Formula used:
Average rate of change of function
Given:
The given function is,
Calculation:
Suppose the two point between which the average rate of change of the linear function is to be calculated is
Substitute
For,
For,
Substitute
Therefore, the average rate of change of linear function
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