Concept explainers
(a)
To state: The increasing / decreasing test.
(a)
Explanation of Solution
The Increasing/decreasing test:
1) If
2) If
(b)
To explain: The meaning of concave upward curve on an interval.
(b)
Explanation of Solution
If graph of a function f lies above all its tangents on interval I then f is known as concave upward over interval I.
In Figure 1, it is shown that for a concave upward curve the tangent lies below the graph of the curve while a concave downward curve the tangent lies above the graph of the curve.
(c)
To state: The concavity test.
(c)
Explanation of Solution
The concavity test:
1) If
2) If
(d)
To define: The inflections points and explain the method of finding them.
(d)
Explanation of Solution
Inflection point:
“A point P on a curve
An inflection point is at
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