a.
To find: The value or the quantity which is depicted by the derivative.
a.
Answer to Problem 29E
The quantity is the speed.
Explanation of Solution
Given information:
The tables of values are as shown below.
Time(t) | Distance(feet) |
0 | 0 |
1 | 3.3 |
2 | 13.3 |
3 | 29.9 |
4 | 53.2 |
5 | 83.2 |
6 | 119.8 |
7 | 163 |
8 | 212.9 |
9 | 269.5 |
10 | 332.7 |
Concept used:
The derivative of the function is obtained by the formula
Calculation:
As the derivative is change in
The
So the change in distance with respect to time is speed.
Conclusion: The speed represents the derivative.
b.
To calculate: The unit of derivative.
b.
Answer to Problem 29E
The unit of distance is
Explanation of Solution
Given information:
The tables of values are as shown below.
Time(t) | Distance(feet) |
0 | 0 |
1 | 3.3 |
2 | 13.3 |
3 | 29.9 |
4 | 53.2 |
5 | 83.2 |
6 | 119.8 |
7 | 163 |
8 | 212.9 |
9 | 269.5 |
10 | 332.7 |
Time(t) | Distance(feet) |
0 | 3.3 |
1 | 13.3 |
2 | 29.9 |
3 | 53.2 |
4 | 83.2 |
5 | 119.8 |
6 | 119.8 |
7 | 163 |
8 | 212.9 |
9 | 269.5 |
10 | 332.7 |
Concept used:
The derivative of the function is obtained by the formula
Calculation:
The derivative is the speed.
The speed is distance divided by time.
The unit of distance is feet and the unit of time is seconds.
Conclusion: The unit of derivative is
c.
To calculate: The graph and equation of derivative.
c.
Answer to Problem 29E
The equation of derivative is
Explanation of Solution
Given information:
The tables of values are as shown below.
Time(t) | Distance(feet) |
0 | 0 |
1 | 3.3 |
2 | 13.3 |
3 | 29.9 |
4 | 53.2 |
5 | 83.2 |
6 | 119.8 |
7 | 163 |
8 | 212.9 |
9 | 269.5 |
10 | 332.7 |
Concept Used:
The derivative of the function is obtained by the formula
Calculation:
Calculation of derivative from the points
For the
The
The one point on the derivative of the function is
x(mid-point) | m(derivative)=y |
0.5 | 3.3 |
1.5 | 10 |
2.5 | 16.6 |
3.5 | 23.3 |
4.5 | 30 |
5.5 | 36.6 |
6.5 | 43.2 |
7.5 | 49.9 |
8.5 | 56.6 |
9.5 | 63.2 |
Graph of the derivative is as shown below.
The value of slope is calculated as shown below.
Conclusion: The derivative of the function is
Chapter 2 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
- 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