Appendix B Lab 5 – Practice Problems
Portland Community College 81
Sketch onto each of figures 1-4 a function that satisfies the properties stated in the caption given
with the figure.
Figure 1
Sketch a function that has a local minimum
at the point
()
3,0 − and whose second
derivative,
f
′′ , has the following
properties.
•
()
0=
′′ xf if 0<x
•
()
0<
′′ xf if 0>x
Figure 3
Sketch a function that passes through
()
2,2− whose first derivative, g′, has
the following properties.
()
0gx
′< if 2−≠x and
()
20g′−=
Figure 4
Sketch a function that passes through
(
)
4,1 , whose first derivative is always
decreasing, and whose first derivative
passes through the point
()
0,1 .
Figure 2
Sketch a function that has a vertical
asymptote at 1−=x, a horizontal
asymptote at 2−=y and whose
second derivative is positive at all
values of x other than 1−=x.
Note: Draw truly asymptotic behavior
at all relevant locations
