Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 5.2, Problem 58E

To determine

To estimate: when Priya is moving toward the motion detector, away from the motion detector.

Expert Solution

Answer to Problem 58E

0≤t≤1.5 : moving towards the motion detector.

2.5≤t≤4.5 : moving away from the motion detector.

5.5≤t≤8

: 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.

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.

0≤t≤1.5 : moving towards the motion detector.

2.5≤t≤4.5 : moving away from the motion detector.

5.5≤t≤8

: 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.

To determine

To give: an interpretation of any local extreme values in term of this problem situation.

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.

To determine

To find: a cubic regression equation for the table data and superimpose its graph on a scatter plot of the data.

Expert Solution

Answer to Problem 58E

D=f(t)=−0.0819505t3+0.916182t2−2.51261t+3.37794.

Explanation of Solution

Calculation:

The cubic regression equation for the table data using graphing utility is:

D=f(t)=−0.0819505t3+0.916182t2−2.51261t+3.37794.

The graph of the above model is shown below.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 5.2, Problem 58E , additional homework tip 1

To determine

To find: a formula for f’ using the model in part (c) and use this formula to estimate the answers to (a).

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: D=f(t)=−0.0819505t3+0.916182t2−2.51261t+3.37794.

Calculation:

f(t)=−0.0819505t3+0.916182t2−2.51261t+3.37794.f'(t)=−0.245852t2+1.83236t−2.51261

The graph of the f’ (t) is shown below.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 5.2, Problem 58E , additional homework tip 2

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 5.2, Problem 57E

Chapter 5.2, Problem 59E

Chapter 5 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 5.1 - Prob. 1QR Ch. 5.1 - Prob. 2QR Ch. 5.1 - Prob. 3QR Ch. 5.1 - Prob. 4QR Ch. 5.1 - Prob. 5QR Ch. 5.1 - Prob. 6QR Ch. 5.1 - Prob. 7QR Ch. 5.1 - Prob. 8QR Ch. 5.1 - Prob. 9QR Ch. 5.1 - Prob. 10QR

Ch. 5.1 - Prob. 11QR Ch. 5.1 - Prob. 12QR Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - 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