14.Letf

(

x

,

y

)

=

1

2

x

y

2

f(x,y)=12xy2

represent the kinetic energy in Joules of an object of massx

x

in kilograms with velocityy

y

in meters per second. Let(

a

,

b

)

(a,b)

be the point(

4

,

5

)

(4,5)

in the domain off

.

f.

1. Calculatef
2. x
3. (
4. a
5. ,
6. b
7. )
8. .
9. fx(a,b).
10. Explain as best you can in the context of kinetic energy what the partial derivative
11. f
12. x
13. (
14. a
15. ,
16. b
17. )
18. =
19. lim
20. h
22. 0
23. f
24. (
25. a
26. +
27. h
28. ,
29. b
30. )
32. f
33. (
34. a
35. ,
36. b
37. )
38. h
39. fx(a,b)=limh0f(a+h,b)f(a,b)h
40. tells us about kinetic energy.
41. Calculatef
42. y
43. (
44. a
45. ,
46. b
47. )
48. .
49. fy(a,b).
50. Explain as best you can in the context of kinetic energy what the partial derivative
51. f
52. y
53. (
54. a
55. ,
56. b
57. )
58. =
59. lim
60. h
62. 0
63. f
64. (
65. a
66. ,
67. b
68. +
69. h
70. )
72. f
73. (
74. a
75. ,
76. b
77. )
78. h
79. fy(a,b)=limh0f(a,b+h)f(a,b)h
80. tells us about kinetic energy.