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

Appendix I Answers to Odd-Numbered Exercises A75
39. (a) The rate at which the percentage of electrical power produced
by solar panels is changing, in percentage points per year.
(b) On January 1, 2002, the percentage of electrical power produced
by solar panels was increasing at a rate of 3.5 percentage
points per year.
41. 24 scornerd; 0 sdiscontinuityd
43. 1 snot definedd; 5 svertical tangentd
45. 2
_2 1
_1
Differentiable at 21;
not differentiable at 0
47. f 99s1d 49. a − f, b − f 9, c − f 99
51. a − acceleration, b − velocity, c − position
Chapter 2 Review • page 166
True-False Quiz
1. False 3. True 5. True 7. False 9. True
11. True 13. True 15. False 17. True
19. True 21. False 23. False 25. True
Exercises
1. (a) (i) 3 (ii) 0 (iii) Does not exist (iv) 2
(v) ` (vi) 2` (vii) 4 (viii) 21
(b) y − 4, y − 21 (c) x − 0, x − 2 (d) 23, 0, 2, 4
3. 1 5. 3 2 7. 3 9. ` 11. 4 7 13. 1 2
15. 2` 17. 2 19. y2 21. x − 0, y − 0 23. 1
29. (a) (i) 3 (ii) 0 (iii) Does not exist
(iv) 0 (v) 0 (vi) 0
(b) At 0 and 3 (c)
y
3
53. 6x 1 2; 6 7
55.
4
f
fª
_4
3
f·
7
f·
f
fªªª
6
_1
fª
4
f 9sxd − 4x 2 3x 2 ,
f 99sxd − 4 2 6x,
f 999sxd − 26,
f s4d sxd − 0
31. R 35. (a) 28 (b) y − 28x 1 17
37. (a) (i) 3 mys (ii) 2.75 mys (iii) 2.625 mys
(iv) 2.525 mys (b) 2.5 mys
39. (a) 10 (b) y − 10x 2 16
(c)
–4
12
–12
4
0
3
x
57. (a) 1 3 a22y3
ca020841
9.4.00
59. f 9sxd −H 21
1
or f 9sxd − x 2 6
| x 2 6 |
if x , 6
if x . 6
y
1
0 6
_1
fª
x
41. (a) The rate at which the cost changes with respect to the
interest rate; dollarsy(percent per year)
(b) As the interest rate increases past 10%, the cost is increasing
at a rate of $1200y(percent per year).
(c) Always positive
43.
y
fª
61. (a)
y (b) All x
(c) f 9sxd − 2| x |
0
x
0
x
45. (a) f 9sxd − 2 5 2 s3 2 5xd21y2 (b) (2`, 3 5 g, (2`, 3 5 )
(c) 6
ca02r33
7.4.00
f
65. (a)
s
(b)
y
y=ds/dt
_3
fª
1
_6
67. 63°
0 3 8 10 15 19 t
0 3 8 10 15 19 t
47. 24 (discontinuity), 21 (corner), 2 (discontinuity),
5 (vertical tangent)
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