13 Nov 2021
Problem 11a
Page 268
Section 4.2: Maximum and Minimum Values
Chapter 4: Applications of Differentiation
Textbook ExpertVerified Tutor
13 Nov 2021
Given information
As per the given question ,
- The function attains its local maximum at
- The function is differentiable at
Step-by-step explanation
Step 1.
The objective is to sketch the graph of a function that has a local maximum at and is differentiable at .
and is differentiable at .Assume the function 
The function is differentiable and calculate the first derivative of the function and equate it to zero to calculate the critical points as,
and equate it to zero to calculate the critical points as,
The function has only one critical point at 
Calculate the second derivative of the function at as follows:
as follows:
Thus, the second derivative at the critical point of the function , is negative and hence local maximum occur at .
of the function , is negative and hence local maximum occur at .
The graph of the function is as shown below:
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