Concept explainers
Whether the statement, if f has an absolute minimum value at c then
Answer to Problem 2RQ
The given statement is false.
Explanation of Solution
Reason:
The given statement as the below example disproves the given statement.
Consider the function,
As f is always non-negative function it has absolute minimum at
But derivative of the function does not exist at
Calculate the derivative of
And similarly,
Thus the left hand limit is not same as the right hand limit.
So,
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