Concept explainers
a)
To sketch: The graph of a function satisfies the following conditions that the graph has two
a)
Explanation of Solution
Let the x be represented in the x-axis and the value of the function
Local maximum is the point in the interval of consideration of the domain at which the function attains its maximum value but not the highest value.
Local minimum is the point in the interval of consideration of the domain at which the function attains its minimum value but not the least value.
Absolute minimum is any point of the domain at which the function attains its minimum value.
Draw the graph of the function
From Figure 1, it is observed that the local
Since the graph has a hole at
b)
To sketch: The graph of a function satisfies the conditions that the graph has three local
b)
Explanation of Solution
Let the x be represented in the x-axis and the value of the function
Local maximum is the point in the interval of consideration of the domain at which the function attains its maximum value but not the highest value. So, consider three local maximum points on the graph.
Local minimum is the point in the interval of consideration of the domain at which the function attains its minimum value but not the least value. So, take two local minimum points on the curve.
Draw the possible graph of the function
From Figure 2, it is observed that the local maximum occurs at two points such that
Also, observe that the critical numbers occurs at
Therefore, including local maxima and minima points there are seven critical numbers.
Thus, the graph has three local minima, two local maxima and seven critical numbers.
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