Concept explainers
Whether the statement, if f is continuous on (a,b) then f attains an absolute maximum value
Explanation of Solution
The given statement is false.
Reason:
Case 1:
If the graph of the function is a line parallel to x-axis, then there will be no absolute minimum or an absolute maximum.
Case 2:
If the graph of the function is a line which is defined on any open interval (a, b), then there will be no absolute minimum or an absolute maximum.
From Figure 1, it can be identified that either the horizontal line or a straight line does not attain its absolute minimum or absolute maximum.
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