To identify: Each curves on the given graph and give proper explanation.
Answer to Problem 43E
The curve c is position curve, b is velocity curve and a is acceleration curve.
Explanation of Solution
Graph:
The given graph is shown as in Figure 1,
Observation:
Observe the graph of b and a carefully.
The point where
Recall that the derivative of a function is zero where the function has a horizontal tangent.
Therefore,
Observe the graph of a and c carefully.
The graph of a has both positive and negative values. Hence a can be either velocity or acceleration.
The points where the graph of a has horizontal tangent, the functional value of c is not zero at that point.
This implies that,
The only possibility is that a is the acceleration curve. This implies that
So,
Thus, c is position curve, b is velocity curve and a is acceleration curve.
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