Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
6th Edition
ISBN: 9781418300203
Author: Prentice Hall
Publisher: Prentice Hall
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Question
Chapter 2.1, Problem 29E
a.
To determine
To find: The value or the quantity which is depicted by the derivative.
a.
Expert Solution
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 determine
To calculate: The unit of derivative.
b.
Expert Solution
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 determine
To calculate: The graph and equation of derivative.
c.
Expert Solution
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
Ch. 2.1 - Prob. 1QRCh. 2.1 - Prob. 2QRCh. 2.1 - Prob. 3QRCh. 2.1 - Prob. 4QRCh. 2.1 - Prob. 5QRCh. 2.1 - Prob. 6QRCh. 2.1 - Prob. 7QRCh. 2.1 - Prob. 8QRCh. 2.1 - Prob. 9QRCh. 2.1 - Prob. 10QR
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Prob. 23ECh. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - Prob. 26ECh. 2.5 - Prob. 27ECh. 2.5 - Prob. 28ECh. 2.5 - Prob. 29ECh. 2.5 - Prob. 30ECh. 2.5 - Prob. 31ECh. 2.5 - Prob. 32ECh. 2.5 - Prob. 33ECh. 2.5 - Prob. 34ECh. 2.5 - Prob. 35ECh. 2.5 - Prob. 36ECh. 2.5 - Prob. 37ECh. 2.5 - Prob. 38ECh. 2.5 - Prob. 39ECh. 2.5 - Prob. 40ECh. 2.5 - Prob. 41ECh. 2.5 - Prob. 42ECh. 2.5 - Prob. 43ECh. 2.5 - Prob. 44ECh. 2.5 - Prob. 45ECh. 2.5 - Prob. 46ECh. 2.5 - Prob. 47ECh. 2.5 - Prob. 48ECh. 2.5 - Prob. 49ECh. 2.5 - Prob. 50ECh. 2.5 - Prob. 51ECh. 2.5 - Prob. 52ECh. 2.5 - Prob. 1QQCh. 2.5 - Prob. 2QQCh. 2.5 - Prob. 3QQCh. 2.5 - Prob. 4QQCh. 2 - Prob. 1RWDTCh. 2 - Prob. 2RWDTCh. 2 - Prob. 3RWDTCh. 2 - Prob. 4RWDTCh. 2 - Prob. 5RWDTCh. 2 - Prob. 6RWDTCh. 2 - Prob. 7RWDTCh. 2 - Prob. 8RWDTCh. 2 - Prob. 9RWDTCh. 2 - Prob. 10RWDTCh. 2 - Prob. 1RECh. 2 - Prob. 2RECh. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - 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Prob. 67RECh. 2 - Prob. 68RECh. 2 - Prob. 69RECh. 2 - Prob. 70RECh. 2 - Prob. 71RECh. 2 - Prob. 72RECh. 2 - Prob. 73RECh. 2 - Prob. 74RECh. 2 - Prob. 75RECh. 2 - Prob. 76RECh. 2 - Prob. 77RECh. 2 - Prob. 78RECh. 2 - Prob. 79RECh. 2 - Prob. 80RECh. 2 - Prob. 81EPCh. 2 - Prob. 82EPCh. 2 - Prob. 83EP
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