6. Given the graph of f, identify the intervals of increasing and decreasing as well as the x coordinates of the relative ex- trema. 20 - 20
6. Given the graph of f, identify the intervals of increasing and decreasing as well as the x coordinates of the relative ex- trema. 20 - 20
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Hi I need help answering question 6, 19, and 31 only thank you.
![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%2Fc0062c03-25f9-43c4-9565-5f5e1496dd63%2Ftfb70bf_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.
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