Concept explainers
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 horizontal tangents at three points. Let these 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 point A to point B, the slope of the graph f is strictly positive which implies that the derivative graph
From the point B to point C, the slope of the graph f is strictly negative which implies that the derivative graph
From the point C to point D, the slope of the graph f is strictly positive which implies that the derivative graph
From the graph, it is observed that the graph has a corner point at one point. Let the point be D. The derivative graph
From the point D to right, the slope of the graph f is strictly negative, which implies that the derivative graph must have a functional value in negative. Since the function is linear in this part, the derivative graph will be horizontal line.
Graph:
Trace the graph of f and use the above information to draw the graph of its derivative directly beneath as shown below in Figure 1.
Thus,
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