51.
53.
55.
(a) C (b) II 57. (a) F (b) I
59. (a) B (b) VI
61. Family of parallel planes
63. Family of hyperboloids of one or two sheets with axis
the y-axis
65. (a) Shift the graph of upward 2 units
(b) Stretch the graph of vertically by a factor of 2
(c) Reflect the graph of about the -plane
(d) Reflect the graph of about the -plane and then shift it
upward 2 units
67.
f appears to have a maximum value of about 15. There are two
local maximum points but no local minimum point.
69.
The function values approach 0 as x, y become large; as
approaches the origin, f approaches or 0, depending on the
direction of approach.
71. If , the graph is a cylindrical surface. For , the level
curves are ellipses. The graph curves upward as we leave the ori-
gin, and the steepness increases as c increases. For , the level
curves are hyperbolas. The graph curves upward in the y-direction
and downward, approaching the xy-plane, in the x-direction giving
a saddle-shaped appearance near (0, 0, 1).
73. 75. (b) y 苷 0.75x 0.01c 苷 2, 0, 2
c
0
c 0c 苷 0
共x, y兲