Whether the statement, there exist a function f such that
Answer to Problem 10RQ
The given statement is false.
Explanation of Solution
Results used:
Concavity test:
(a)If a function is such that
(b) If a function is such that
It is given that
Also, as
From concavity test, as
If the graph is concave upward then the graph must cross the x-axis at some point as x approaches infinity.
This implies that the function is positive. So, this is not possible.
Hence, 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