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30 Dec 2021
Problem 65a
Page 270
Section 4.2: Maximum and Minimum Values
Chapter 4: Applications of Differentiation
Textbook ExpertVerified Tutor
30 Dec 2021
Given information
Given the interval of following question 
Step-by-step explanation
Step 1.
A mathematical model of coughing is given as the function 
(velocity) of the airstream, and it is related to the radius 
of the trachea. Function is
(velocity) of the airstream, and it is related to the radius of the trachea. Function is
To find an absolute maximum of the function on the interval , we use The Closed Method Interval. So we find derivative of the given function and see where it is equal to zero or where the function 
is undefined. Also, we find the values of at the endpoints of the interval. Hence, using the Product Rule for derivatives, we have:
on the interval , we use The Closed Method Interval. So we find derivative of the given function and see where it is equal to zero or where the function is undefined. Also, we find the values of at the endpoints of the interval. Hence, using the Product Rule for derivatives, we have:
Now we find where 
:
:
Now we find and compare the values of the function at 
and 
and at the endpoints of the interval:
at and and at the endpoints of the interval:
The largest of the values is the absolute maximum value and it is at
which agrees with the with experimental evidence in the exercise.
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805
Solutions
Chapter
Section
- Problem 1
- Problem 2a
- Problem 2b
- Problem 3
- Problem 4
- Problem 5
- Problem 6
- Problem 7
- Problem 8
- Problem 9
- Problem 10
- Problem 11a
- Problem 11c
- Problem 11c
- Problem 12a
- Problem 12b
- Problem 13a
- Problem 13b
- Problem 14a
- Problem 14b
- Problem 15
- Problem 16
- Problem 17
- Problem 18
- Problem 19
- Problem 20
- Problem 21
- Problem 22
- Problem 23
- Problem 24
- Problem 25
- Problem 26
- Problem 27
- Problem 28
- Problem 29
- Problem 30
- Problem 31
- Problem 32
- Problem 33
- Problem 34
- Problem 35
- Problem 36
- Problem 37
- Problem 38
- Problem 39
- Problem 40
- Problem 41
- Problem 42
- Problem 43
- Problem 44
- Problem 45
- Problem 46
- Problem 47
- Problem 48
- Problem 49
- Problem 50
- Problem 51
- Problem 52
- Problem 53
- Problem 54
- Problem 55
- Problem 56
- Problem 57a
- Problem 57b
- Problem 58a
- Problem 58b
- Problem 59a
- Problem 59b
- Problem 60a
- Problem 60b
- Problem 61
- Problem 62
- Problem 63
- Problem 64a
- Problem 64b
- Problem 65a
- Problem 65b
- Problem 65c
- Problem 66a
- Problem 66b