Concept explainers
To prove: Relation between slope and average rate of change.
Answer to Problem 102E
Average rate of change is analogous to the slope at a point.
Explanation of Solution
Given information: Slope and average rate of change.
Formula used: Rate of change =
The slope is defined as the ratio of the vertical change between two points, the rise and horizontal change between the same two points, the run.
The rate of change of a function is a ratio that compares the differences between two output values to the differences between the corresponding input values.
Rate of change Formula helps us to calculate the slope of a line if the coordinates of the points on the line are given.
In other words, Average rate of change is analogous to the slope at a point.If the graph of a function is not linear, the average rate of change is found by finding the slope of the secant line that passes through the graph twice.
Chapter 1 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
- 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