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
Question
23 and 29
![2(7 – x)
49. y = 2x³
= (x)f
x²
-x+て
%3D
(x – 1)4
51. y = 16x
-
%3D
2(2x + 1)
53. y = 3x4
4. f(x) =
(x – 1)4
6(3x2 + 2)
55. y = 4x²
57. y = x'/
59. y = 4x
(x – 1)2if"(x) .
%3D
%3D
|
5. f(x)
%3D
(x2 – 2)3
x(2x² – 3a?)
%3D
|
= (x),,f:zx – zv^x = (x)f *9
(a² – x²)3/2
61. y = 2x
%3D
-
%D
%3D
In Problems 7–34, determine concavity and the x-values where
points of inflection occur. Do not sketch the graphs.
463. Sketch
f(2) = 4, ƒ
7. y = -2x2 + 4x
9. y = 4x3 + 12x2 – 12x
11. y = ax + bx² + cx + d
8. y = -74x2 + 19x – 37
10. y = x³ – 6x² + 9x + 1
64. Sketch
ƒ(4) = 4, f
%3D
-
12. y = x – 8x² – 6
9x2
+ 2x
65. Sketch
f(1) = 1,f
|
13. y = 2x4 – 48x2 + 7x + 3 14. y =
66. Sketch
f(1) = 1, b
f(x) > 0 ar
%3D
4.
2.
odT.(2.1) 18 16. y =
ec2 tu
15. y = 2x'/5
%3D
%3D
7x²
+x +5
17. y =
67. Dema
%3D
9.
2.
equation p
5.
18. y = --x
1.
2
1.
|
68. Avera
2.
19. y =
20
1.
X-
2 3
st.
4.
-
-
-
4'
- 3x + 17x + 43
10
1.
21. y =
7.
x²+6x² +5x – 4
show that
-
30
12
concave u
x + 1
22. y = x6 - 3x4
23. y =
69. Speci
x - 1
x²
25. y =
may depe:
1.
24. y = 1 -
x²
we see tha
the left pl
there are f
x2 +1
ax²
21x + 40
27. y =
6(x+3)2
%3D
9+x
28. y = 3(x² – 2)²
29. y = 5e
%3D
30. y = e – e*
31. y = axe
32. y = xe
33. y =
2x
34. y =
3e
ter?
In Problems 35-62, determine intervals on which the function
is increasing, decreasing, concave up, and concave down; relative
maxima and minima; inflection points; symmetry; and those
intercepts that can be obtained conveniently. Then sketch the graph.
35](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e2d6f28-e3d7-414c-b1d4-a752131175c2%2F38d0f94b-4b02-4e72-b26b-5966b9707df1%2Fxel8yv4.jpeg&w=3840&q=75)
Transcribed Image Text:2(7 – x)
49. y = 2x³
= (x)f
x²
-x+て
%3D
(x – 1)4
51. y = 16x
-
%3D
2(2x + 1)
53. y = 3x4
4. f(x) =
(x – 1)4
6(3x2 + 2)
55. y = 4x²
57. y = x'/
59. y = 4x
(x – 1)2if"(x) .
%3D
%3D
|
5. f(x)
%3D
(x2 – 2)3
x(2x² – 3a?)
%3D
|
= (x),,f:zx – zv^x = (x)f *9
(a² – x²)3/2
61. y = 2x
%3D
-
%D
%3D
In Problems 7–34, determine concavity and the x-values where
points of inflection occur. Do not sketch the graphs.
463. Sketch
f(2) = 4, ƒ
7. y = -2x2 + 4x
9. y = 4x3 + 12x2 – 12x
11. y = ax + bx² + cx + d
8. y = -74x2 + 19x – 37
10. y = x³ – 6x² + 9x + 1
64. Sketch
ƒ(4) = 4, f
%3D
-
12. y = x – 8x² – 6
9x2
+ 2x
65. Sketch
f(1) = 1,f
|
13. y = 2x4 – 48x2 + 7x + 3 14. y =
66. Sketch
f(1) = 1, b
f(x) > 0 ar
%3D
4.
2.
odT.(2.1) 18 16. y =
ec2 tu
15. y = 2x'/5
%3D
%3D
7x²
+x +5
17. y =
67. Dema
%3D
9.
2.
equation p
5.
18. y = --x
1.
2
1.
|
68. Avera
2.
19. y =
20
1.
X-
2 3
st.
4.
-
-
-
4'
- 3x + 17x + 43
10
1.
21. y =
7.
x²+6x² +5x – 4
show that
-
30
12
concave u
x + 1
22. y = x6 - 3x4
23. y =
69. Speci
x - 1
x²
25. y =
may depe:
1.
24. y = 1 -
x²
we see tha
the left pl
there are f
x2 +1
ax²
21x + 40
27. y =
6(x+3)2
%3D
9+x
28. y = 3(x² – 2)²
29. y = 5e
%3D
30. y = e – e*
31. y = axe
32. y = xe
33. y =
2x
34. y =
3e
ter?
In Problems 35-62, determine intervals on which the function
is increasing, decreasing, concave up, and concave down; relative
maxima and minima; inflection points; symmetry; and those
intercepts that can be obtained conveniently. Then sketch the graph.
35
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