Concept explainers
To find: The critical number of the function
Answer to Problem 31E
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)
Power Rule:
If n is positive integer, then
Calculation:
Obtain the first derivative of the given function
Apply the power rule as shown in equation (1).
Set
Squaring on both sides,
The value of
That is, the value of
Hence, it satisfies the condition of critical number definition. Therefore, the critical number exist at
Thus, the critical number 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