Concept explainers
To sketch: The graph of
Answer to Problem 14E
The formula for
Explanation of Solution
The given function is
Recall the fact that, the derivative of a function at
From the graph, it is observed that the graph has a horizontal tangent at three points. Let the points be A, B, C and D. At these points, the derivative will be zero.
The AB section of the graph has negative slope which implies that the derivative will be negative in the section.
The BC section of the graph has positive slope which implies that the derivative will be positive in the section.
The CD section of the graph has negative slope which implies that the derivative will be negative in the section.
Graph:
Use the online graphing calculator to draw the graph of
Observation:
From the Figure 1, it is observed that the graph of the derivative function seems to be the cosine function.
Thus, the formula of the derivative function is,
Chapter 2 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