To find: The second degree polynomial.
Answer to Problem 61E
The second degree polynomial is
Explanation of Solution
Given:
The second degree polynomial satisfies
Derivative rules:
(1) Constant multiple rule:
(2) Power rule:
(3)
Calculation:
The general form of the second degree polynomial is
Obtain the first derivative of
Apply the sum rule (3) and the constant multiple (1),
Since the derivative of constant function is zero,
Apply the power rule (2) and simplify the terms,
Therefore, the first derivative of
Obtain the second derivative of
Apply the sum rule (3) and the constant multiple (1),
Since the derivative of constant function is zero,
Apply the power rule (2) and simplify the terms,
Therefore, the second derivative of
Obtain the second degree polynomial P.
Substitute 2 for x in
Since
Thus, the value of
Substitute 2 for x in
Since
Thus, the value of
Substitute 2 for x in
Since
Thus, the value of
Substitute the values 1 for a,-1 for b and 3 for c in
Therefore, the second degree polynomial is
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