Concept explainers
To find: The critical number of the function
Answer to Problem 33E
The critical number of the function
Explanation of Solution
Definition used:
A critical number of a function f is a number c, if it satisfies either of the below conditions:
(1)
(2)
The Product Rule:
If two functions
Calculation:
Obtain the first derivative of the given function.
Apply the product rule as shown in equation (1).
Simplify further as follows.
Set
Therefore, the solutions are
The derivative function
Hence, it satisfies the condition of the critical number definition. Therefore, the critical number occurs at
Thus, the critical numbers of the function
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