Calculus: Graphical, Numerical, Algebraic
3rd Edition
ISBN: 9780133688399
Author: Finney, Ross L.
Publisher: Pearson/Prentice Hall
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Question
Chapter 5.2, Problem 58E
a.
To determine
To estimate: when Priya is moving toward the motion detector, away from the motion detector.
a.
Expert Solution
Answer to Problem 58E
: moving towards the motion detector again.
Between 1.5 and 2.5 there is a
t = 2.
Between 4.5 and 5.5 there is a
t = 5.
Explanation of Solution
Given information: Priya’s distance D in meters from a motion detector is given by the
data in below table.
| t (sec) | D (m) | t (sec) | D (m) |
| 0.0 | 3.36 | 4.5 | 3.59 |
| 0.5 | 2.61 | 5.0 | 4.15 |
| 1.0 | 1.86 | 5.5 | 3.99 |
| 1.5 | 1.27 | 6.0 | 3.37 |
| 2.0 | 0.91 | 6.5 | 2.58 |
| 2.5 | 1.14 | 7.0 | 1.93 |
| 3.0 | 1.69 | 7.5 | 1.25 |
| 3.5 | 2.37 | 8.0 | 0.67 |
| 4.0 | 3.01 |
Calculation:
D (t) is increasing when Priya is moving away and decreasing when moving towards the motion detector.
: moving towards the motion detector again.
Between 1.5 and 2.5 there is a local minimum, but cannot be sure about the direction at
t = 2.
Between 4.5 and 5.5 there is a local maximum, but cannot be sure about the direction at
t = 5.
b.
To determine
To give: an interpretation of any local extreme values in term of this problem situation.
b.
Expert Solution
Answer to Problem 58E
At t = 2 Priya is at relative minimum distance to the detector . At t = 5 Priya is at a relative maximum distance from the detector.
Explanation of Solution
Calculation:
At t = 2 Priya is at relative minimum distance to the detector . At t = 5 Priya is at a relative maximum distance from the detector.
c.
To determine
To find: a cubic regression equation for the table data and superimpose its graph on a
c.
Expert Solution
Answer to Problem 58E
Explanation of Solution
Calculation:
The cubic regression equation for the table data using graphing utility is:
The graph of the above model is shown below.
d.
To determine
To find: a formula for f’ using the model in part (c) and use this formula to estimate the answers to (a).
d.
Expert Solution
Answer to Problem 58E
Interval:
(0, 1.8) − moving towards door.
(1.8, 5.6) − moving away.
(5.6, 8) − moving towards.
Explanation of Solution
Given information:
Calculation:
The graph of the f’ (t) is shown below.
From the graph:
When f’ (t) < 0 .the distance f (t) is decreasing.
When f’ (t) >0 . the distance f (t) is increasing.
Interval:
(0, 1.8) − moving towards door.
(1.8, 5.6) − moving away.
(5.6, 8) − moving towards.
Chapter 5 Solutions
Calculus: Graphical, Numerical, Algebraic
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