James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

302 Chapter 4 Applications of Differentiation
35–36 The graph of the derivative f 9 of a continuous function f
is shown.
(a) On what intervals is f increasing? Decreasing?
(b) At what values of x does f have a local maximum? Local
minimum?
(c) On what intervals is f concave upward? Concave downward?
(d) State the x-coordinate(s) of the point(s) of inflection.
(e) Assuming that f s0d − 0, sketch a graph of f.
35.
y
36.
2
0 2 4 6 8 x
_2
y
2
_2
y=fª(x)
y=fª(x)
0 x
2 4 6 8
37–48
(a) Find the intervals of increase or decrease.
(b) Find the local maximum and minimum values.
(c) Find the intervals of concavity and the inflection points.
(d) Use the information from parts (a)–(c) to sketch the graph.
Check your work with a graphing device if you have one.
37. f sxd − x 3 2 12x 1 2 38. f sxd − 36x 1 3x 2 2 2x 3
39. f sxd − 1 2 x 4 2 4x 2 1 3 40. tsxd − 200 1 8x 3 1 x 4
41. hsxd − sx 1 1d 5 2 5x 2 2 42. hsxd − 5x 3 2 3x 5
43. Fsxd − xs6 2 x
45. Csxd − x 1y3 sx 1 4d
47. f sd − 2 cos 1 cos 2 , 0 < < 2
48. Ssxd − x 2 sin x, 0 < x < 4
44. Gsxd − 5x 2y3 2 2x 5y3
46. f sxd − lnsx 2 1 9d
49–56
(a) Find the vertical and horizontal asymptotes.
(b) Find the intervals of increase or decrease.
(c) Find the local maximum and minimum values.
(d) Find the intervals of concavity and the inflection points.
(e) Use the information from parts (a)–(d) to sketch the graph
of f.
49. f sxd − 1 1 1 x 2 1 x 50. f sxd − x 2 2 4
2 x 2 1 4
51. f sxd − sx 2 1 1 2 x 52. f sxd − e x
1 2 e x
53. f sxd − e 2x 2 54. f sxd − x 2 1 6 x 2 2 2 3 ln x
55. f sxd − lns1 2 ln xd
56. f sxd − e arctan x
57. Suppose the derivative of a function f is
f 9sxd − sx 1 1d 2 sx 2 3d 5 sx 2 6d 4 . On what interval is f
increasing?
58. Use the methods of this section to sketch the curve
y − x 3 2 3a 2 x 1 2a 3 , where a is a positive constant. What
do the members of this family of curves have in common?
How do they differ from each other?
; 59–60
(a) Use a graph of f to estimate the maximum and minimum
values. Then find the exact values.
(b) Estimate the value of x at which f increases most rapidly.
Then find the exact value.
59. f sxd − x 1 1
60. f sxd − x 2 e 2x
sx 2 1 1
;
CAS
61–62
(a) Use a graph of f to give a rough estimate of the intervals of
concavity and the coordinates of the points of inflection.
(b) Use a graph of f 0 to give better estimates.
61.
f sxd − sin 2x 1 sin 4x, 0 < x <
62. f sxd − sx 2 1d 2 sx 1 1d 3
63–64 Estimate the intervals of concavity to one decimal place
by using a computer algebra system to compute and graph f 0.
63. f sxd − x 4 1 x 3 1 1
sx 2 1 x 1 1
64. f sxd − x 2 tan 21 x
1 1 x 3
65. A graph of a population of yeast cells in a new laboratory
culture as a function of time is shown.
Number
of
yeast cells
700
600
500
400
300
200
100
0 2 4 6 8 10 12 14 16 18
Time (in hours)
(a) Describe how the rate of population increase varies.
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