Whether the statement “There exists a function f such that
Answer to Problem 8RQ
The given statement is false.
Explanation of Solution
Result used:
Mean value theorem:
If f is a continuous function on
Calculation:
Given statement is false since the following example disproves it.
Consider the two points
The slope of the line joining these points is given by
Note that the slope represents the first derivative of the function.
Thus, there exists some point c in
Therefore
Therefore, the given statement is false.
Chapter 4 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced 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