Concept explainers
To show: The function
Explanation of Solution
Derivative rules:
(1) Constant multiple rule:
(2) Product rule:
(3)
Proof:
Obtain the first derivative of
Apply the sum rule (3) and the constant multiple rule (1),
Apply the product rule (2),
Therefore, the first derivative of
Obtain the second derivative of
Apply the product rule (2),
Therefore, the second derivative of
Substitute the values of
Simplify further,
Hence, the function
Chapter 3 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