Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Topic Video
Question
Hi I need help answering number 9.
![1. In your own words describe what it means for a function to
be increasing.
2
2. What does a decreasing function "look like"?
-2
3. Sketch a graph of a function on [0, 2] that is increasing but
not strictly increasing.
-2
4. Give an example of a function describing a situation where
it is "bad" to be increasing and "good" to be decreasing.
-4
9. Given the graph of f', identify the intervals of increasing
and decreasing as well as the x coordinates of the relative
5. A function f has derivative f' (x) = (sin x+ 2)e* +1, where
f'(x) > 1 for all x. Is f increasing, decreasing, or can we
not tell from the given information?
extrema.
Problems
6. Given the graph of f, identify the intervals of increasing and
decreasing as well as the x coordinates of the relative ex-
trema.
In Exercises 10–17, a function f(x) is given.
y
(a) Compute f'(x).
20
(b) Graph f and f' on the same axes (using technology is
permitted) and verify Theorem 26.
10. f(x) = 2x + 3
11. f(x) — х — 3х + 5
12. f(x) = cos X
13. f(x) = tan x
14. f(x) — х —5x + 7х— 1
- 20
15. f(x) = 2x – x + x – 1
16. f(x) — х — 5x? + 4
7. Given the graph of f, identify the intervals of increasing and
decreasing as well as the x coordinates of the relative ex-
1
17. f(x) =
x2 + 1
trema.
y
In Exercises 18–38, a function f(x) is given.
(a) Give the domain of f.
2
(b) Find the critical numbers of f.
(c) Create a number line to determine the intervals on
which f is increasing and decreasing.
1
(d) Use the First Derivative Test to determine whether each
critical point is a relative maximum, minimum, or nei-
ther.
27
18. f(x) = x + 2x – 3
167
19. f(x) = x + 3x² + 3
20. f(x) = 2x +x – x+ 3
31. f(x) = (x² – 1)³
32. f(x) = x'/³ (x + 4)
21. f(x) — х — 3x2 + 3х— 1
33. f(0) = 2 cos 0 + cos? 0 on [o, 27]
1
22. f(x) =
34. f(x) = 2/x – 4x²
x² – 2x + 2
x2 - 4
35. f(x) = 5x?/3 – 2x/3
23. f(x) =
36. f(x) = x* – 4x² + 3
37. f(x) = sin³ x on [0, 27]
x2 – 1
24. f(x)
x²
2х— 8
38. f(x) 3 (х + 1)5 — 5х — 2
(x – 2)2/3
25. f(x) =
26. f(x) = sin x cos x on (-T, T).
Review
27. f(x) = x° – 5x
39. Consider f(x) = x² – 3x + 5 on [–1, 2]; findc guaranteed
by the Mean Value Theorem.
28. f(x) = x – 2 sin x on 0 < x < 3T
29. f(x) = cos² x – 2 sin x on 0 < x< 27
30. f(х) — х/x - 3
40. Consider f(x) = sinx on [-T/2, 7/2]; find c guaranteed
by the Mean Value Theorem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf266520-407e-4b51-839c-e1d92d759be6%2F7f8f5786-9d18-4c50-ad1d-1bfc2d47fdb5%2Fi7oat8yk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. In your own words describe what it means for a function to
be increasing.
2
2. What does a decreasing function "look like"?
-2
3. Sketch a graph of a function on [0, 2] that is increasing but
not strictly increasing.
-2
4. Give an example of a function describing a situation where
it is "bad" to be increasing and "good" to be decreasing.
-4
9. Given the graph of f', identify the intervals of increasing
and decreasing as well as the x coordinates of the relative
5. A function f has derivative f' (x) = (sin x+ 2)e* +1, where
f'(x) > 1 for all x. Is f increasing, decreasing, or can we
not tell from the given information?
extrema.
Problems
6. Given the graph of f, identify the intervals of increasing and
decreasing as well as the x coordinates of the relative ex-
trema.
In Exercises 10–17, a function f(x) is given.
y
(a) Compute f'(x).
20
(b) Graph f and f' on the same axes (using technology is
permitted) and verify Theorem 26.
10. f(x) = 2x + 3
11. f(x) — х — 3х + 5
12. f(x) = cos X
13. f(x) = tan x
14. f(x) — х —5x + 7х— 1
- 20
15. f(x) = 2x – x + x – 1
16. f(x) — х — 5x? + 4
7. Given the graph of f, identify the intervals of increasing and
decreasing as well as the x coordinates of the relative ex-
1
17. f(x) =
x2 + 1
trema.
y
In Exercises 18–38, a function f(x) is given.
(a) Give the domain of f.
2
(b) Find the critical numbers of f.
(c) Create a number line to determine the intervals on
which f is increasing and decreasing.
1
(d) Use the First Derivative Test to determine whether each
critical point is a relative maximum, minimum, or nei-
ther.
27
18. f(x) = x + 2x – 3
167
19. f(x) = x + 3x² + 3
20. f(x) = 2x +x – x+ 3
31. f(x) = (x² – 1)³
32. f(x) = x'/³ (x + 4)
21. f(x) — х — 3x2 + 3х— 1
33. f(0) = 2 cos 0 + cos? 0 on [o, 27]
1
22. f(x) =
34. f(x) = 2/x – 4x²
x² – 2x + 2
x2 - 4
35. f(x) = 5x?/3 – 2x/3
23. f(x) =
36. f(x) = x* – 4x² + 3
37. f(x) = sin³ x on [0, 27]
x2 – 1
24. f(x)
x²
2х— 8
38. f(x) 3 (х + 1)5 — 5х — 2
(x – 2)2/3
25. f(x) =
26. f(x) = sin x cos x on (-T, T).
Review
27. f(x) = x° – 5x
39. Consider f(x) = x² – 3x + 5 on [–1, 2]; findc guaranteed
by the Mean Value Theorem.
28. f(x) = x – 2 sin x on 0 < x < 3T
29. f(x) = cos² x – 2 sin x on 0 < x< 27
30. f(х) — х/x - 3
40. Consider f(x) = sinx on [-T/2, 7/2]; find c guaranteed
by the Mean Value Theorem.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images

Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you

Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning

Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON

Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON

Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning

Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON

Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON

Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman


Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning