Concept explainers
Trace or copy the graph of the given function .f. (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of f' below it.
Example 1
FIGURE 1
FIGURE 2
To sketch: The graph of derivative of f below the graph of f.
Explanation of Solution
From the given graph, it is observed that the graph of f contains the horizontal tangents at the three points. Let the three points be A, B and C.
Note that, the value of the derivative will be zero at the point where the function has the horizontal tangent.
Thus, the graph of
From the point A to left, the slope of the graph f is strictly negative which implies that the derivative graph
From the points between A and B, the slope of the graph f is strictly positive which implies that the derivative graph
And, the slope of the graph f between the points B and C is strictly negative, which implies that the derivative graph
From point C to right, the slope of the graph f is strictly positive, which implies that the derivative graph must have a positive functional value.
Use the above information and obtain the graph of
From Figure1, it is observed that the function
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