3.3 Increasing and Decreasing Functions and the First Derivative Test 187 3.3 Exercises See CalcChat.com for tutorial help and worked-out solutions to odd-numbered exercises. CK Intervals on Which a Function Is Increasing or Decreasing In Exercises 11-18, find the open intervals on which the function is increasing or decreasing. 1. Increasing and Decreasing Functions Describe the Test reasing and Decreasing Functions in your CONCEPT ity, ion et. Own wo 11. g(x) x2- 2x 8 2. First Derative Test Describe the First Derivative 12. h(x) 12x - Test in yuwn words. 13. y x/16 - nd 9 14. y x + - Using a Graph in Exercises 3 and 4, use the graph off to find (a) the larEet open interval on which f is increasing and (b) the largest open interval on which f is decreasing. 15. f(x)= sin x - 1, 0< x < 2T Зx 16. f(x) = cos 0 < x < 2 2 17. y x- 2 cos x, 0 < x < 27T 4. У 3. 18. f(x) sin2 x +sin x, 0 < x < 27t 6 10 8 Applying the First Derivative Test In Exercises 19-40, (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is increasing or decreasing, (c) apply the First Derivative Test to identify all relative extrema, and (d) use a graphing utility to confirm your 2 6 4+ 2 2- х 4 6 8 10 results. Using a Graph In Exercises 5-10, use the graph to estimate the open intervals on which the function is increasing or decreasing. Then find the open intervals analytically. 19. f(x) x2-8x 20. f(x) x2 + 6x + 10 21. f(x) =-2x2 4x + 3 22. f(x) -3x2- 4x - 2 23. f(x) =-7x3 + 21x + 3 24. f(x) x3- 6x2 +15 25. f(x) (x - 1)2(x +3) 26. f(x) = (8- x)(x + 1)2 6. f(x) x2- 6x + 8 5. y (x + 1)2 x5-5x -x6 + 6x 27. f(x) = 5 28. f(x) = у у 10 4 + X 29. f(x) x1/3 + 1 30. f(x) x2/3 - 4 -3 1 -1 -1 3 32. f(x) (x 3)1/3 34. f(x) x + 3| - 1 31. f(x) = (x + 2)2/3 2 -2 33. f(x) 5- x - 5 1 -3 x 1 х 4 5 2 35. f(x) 2x + 36. f) = 1 AT x-5 X x2- 2x + 1 38. f(x) = 37. f(x) = 8. f(x) xt- 2r 7. y= Зx x2-9 (2x + 1, x s -1 2-2, x> -1 4 -x, x 0 У у 40. f(x) 11 39. f(x) = AV -2x, Applying the First Derivative Test In Exercises 41-48, consider the function on the interval (0, 2). (a) Find the open intervals on which the function is increasing or decreasing. (b) Apply the First Derivative Test to identify all relative extrema. (c) Use a graphing utility to confirm your results. 2 + -2 -2 4 X + -2 2 1 9. flx) 10. y 2x 1 x+1) 42. f(x) = sin x cos x + 5 41. f(x) x- 2 sin x 44. f(x) =+cosx 43. f(x) = sin x + cos x 46. fx) = sinx -cos x sin x 45. f) cos (2x) 48. flx) = - 1 + cos?x 47. f(x) sinx + sin x -4-3-2-1 FORATED FOR 4 17 2
3.3 Increasing and Decreasing Functions and the First Derivative Test 187 3.3 Exercises See CalcChat.com for tutorial help and worked-out solutions to odd-numbered exercises. CK Intervals on Which a Function Is Increasing or Decreasing In Exercises 11-18, find the open intervals on which the function is increasing or decreasing. 1. Increasing and Decreasing Functions Describe the Test reasing and Decreasing Functions in your CONCEPT ity, ion et. Own wo 11. g(x) x2- 2x 8 2. First Derative Test Describe the First Derivative 12. h(x) 12x - Test in yuwn words. 13. y x/16 - nd 9 14. y x + - Using a Graph in Exercises 3 and 4, use the graph off to find (a) the larEet open interval on which f is increasing and (b) the largest open interval on which f is decreasing. 15. f(x)= sin x - 1, 0< x < 2T Зx 16. f(x) = cos 0 < x < 2 2 17. y x- 2 cos x, 0 < x < 27T 4. У 3. 18. f(x) sin2 x +sin x, 0 < x < 27t 6 10 8 Applying the First Derivative Test In Exercises 19-40, (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is increasing or decreasing, (c) apply the First Derivative Test to identify all relative extrema, and (d) use a graphing utility to confirm your 2 6 4+ 2 2- х 4 6 8 10 results. Using a Graph In Exercises 5-10, use the graph to estimate the open intervals on which the function is increasing or decreasing. Then find the open intervals analytically. 19. f(x) x2-8x 20. f(x) x2 + 6x + 10 21. f(x) =-2x2 4x + 3 22. f(x) -3x2- 4x - 2 23. f(x) =-7x3 + 21x + 3 24. f(x) x3- 6x2 +15 25. f(x) (x - 1)2(x +3) 26. f(x) = (8- x)(x + 1)2 6. f(x) x2- 6x + 8 5. y (x + 1)2 x5-5x -x6 + 6x 27. f(x) = 5 28. f(x) = у у 10 4 + X 29. f(x) x1/3 + 1 30. f(x) x2/3 - 4 -3 1 -1 -1 3 32. f(x) (x 3)1/3 34. f(x) x + 3| - 1 31. f(x) = (x + 2)2/3 2 -2 33. f(x) 5- x - 5 1 -3 x 1 х 4 5 2 35. f(x) 2x + 36. f) = 1 AT x-5 X x2- 2x + 1 38. f(x) = 37. f(x) = 8. f(x) xt- 2r 7. y= Зx x2-9 (2x + 1, x s -1 2-2, x> -1 4 -x, x 0 У у 40. f(x) 11 39. f(x) = AV -2x, Applying the First Derivative Test In Exercises 41-48, consider the function on the interval (0, 2). (a) Find the open intervals on which the function is increasing or decreasing. (b) Apply the First Derivative Test to identify all relative extrema. (c) Use a graphing utility to confirm your results. 2 + -2 -2 4 X + -2 2 1 9. flx) 10. y 2x 1 x+1) 42. f(x) = sin x cos x + 5 41. f(x) x- 2 sin x 44. f(x) =+cosx 43. f(x) = sin x + cos x 46. fx) = sinx -cos x sin x 45. f) cos (2x) 48. flx) = - 1 + cos?x 47. f(x) sinx + sin x -4-3-2-1 FORATED FOR 4 17 2
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...
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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Topic Video
Question
41

Transcribed Image Text:3.3
Increasing and Decreasing Functions and the First Derivative Test
187
3.3 Exercises
See CalcChat.com for tutorial help and worked-out solutions to odd-numbered exercises.
CK
Intervals on Which a Function Is Increasing
or Decreasing In Exercises 11-18, find the
open intervals on which the function is increasing
or decreasing.
1. Increasing and Decreasing Functions Describe
the Test reasing and Decreasing Functions in your
CONCEPT
ity,
ion
et.
Own wo
11. g(x) x2- 2x 8
2. First Derative Test Describe the First Derivative
12. h(x) 12x -
Test in yuwn words.
13. y x/16 -
nd
9
14. y x + -
Using a Graph in Exercises 3 and 4, use the graph off to
find (a) the larEet open interval on which f is increasing and
(b) the largest open interval on which f is decreasing.
15. f(x)= sin x - 1, 0< x < 2T
Зx
16. f(x) = cos
0 < x < 2
2
17. y
x- 2 cos x, 0 < x < 27T
4.
У
3.
18. f(x) sin2 x +sin x, 0 < x < 27t
6
10
8
Applying the First Derivative Test In
Exercises 19-40, (a) find the critical numbers of
f, if any, (b) find the open intervals on which the
function is increasing or decreasing, (c) apply the
First Derivative Test to identify all relative extrema,
and (d) use a graphing utility to confirm your
2
6
4+
2
2-
х
4 6 8 10
results.
Using a Graph In Exercises 5-10, use the
graph to estimate the open intervals on which the
function is increasing or decreasing. Then find the
open intervals analytically.
19. f(x) x2-8x
20. f(x) x2 + 6x + 10
21. f(x) =-2x2 4x + 3
22. f(x) -3x2- 4x - 2
23. f(x) =-7x3 + 21x + 3
24. f(x) x3- 6x2 +15
25. f(x) (x - 1)2(x +3)
26. f(x) = (8- x)(x + 1)2
6. f(x) x2- 6x + 8
5. y (x + 1)2
x5-5x
-x6 + 6x
27. f(x) =
5
28. f(x) =
у
у
10
4
+
X
29. f(x) x1/3 + 1
30. f(x) x2/3 - 4
-3
1
-1
-1
3
32. f(x) (x 3)1/3
34. f(x) x + 3| - 1
31. f(x) = (x + 2)2/3
2
-2
33. f(x) 5- x - 5
1
-3
x
1
х
4 5
2
35. f(x) 2x +
36. f) =
1
AT
x-5
X
x2- 2x + 1
38. f(x) =
37. f(x) =
8. f(x) xt- 2r
7. y=
Зx
x2-9
(2x + 1, x s -1
2-2, x> -1
4 -x, x 0
У
у
40. f(x)
11
39. f(x) =
AV
-2x,
Applying the First Derivative Test In
Exercises 41-48, consider the function on the
interval (0, 2). (a) Find the open intervals on
which the function is increasing or decreasing.
(b) Apply the First Derivative Test to identify
all relative extrema. (c) Use a graphing utility to
confirm your results.
2
+
-2
-2
4
X
+
-2
2
1
9. flx)
10. y
2x 1
x+1)
42. f(x) = sin x cos x + 5
41. f(x) x- 2 sin x
44. f(x) =+cosx
43. f(x) = sin x + cos x
46. fx) = sinx -cos x
sin x
45. f) cos (2x)
48. flx) =
-
1 + cos?x
47. f(x) sinx + sin x
-4-3-2-1
FORATED FOR
4
17
2
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