Name______________________ MTH 251/Lab 5 Graded Homework
Page 1 of 2
Activity 3
Sketch onto Figure 3 a function that satisfies each of
the following properties.
• The function is everywhere continuous.
•
()
0>
′xf on −3, 2
(
)
.
•
()
0<
′xf on −∞,−3
(
)
, 2,4
(
)
, and 4,
∞
(
)
.
•
() ()
043 =
′
=−
′ff
•
()
0>
′′ xf on −∞,2
(
)
and 2,4
(
)
.
•
()
0<
′′ xf on 4,∞
(
)
.
•
()
20 =f
Activity 4
• Sketch onto Figure 4 a function that is everywhere continuous and whose first derivative
function is always positive and always decreasing; draw the function so that
()
(
)
100
=
′
=ff .
• Sketch onto Figure 5 a function that has vertical asymptotes at 2−
=
x and 3=x (but no
other discontinuities) and whose first derivative value continually increases on each of the
intervals −∞,−2
(
)
, −2,3
(
)
, and 3,
∞
(
)
.
1 2 3 4 5 6-1-2-3-4-5-6
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
x
y
Figure 3:
()
xfy
=
1 2 3 4 5 6-1-2-3-4-5-6
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
x
y
Figure 4:
()
xfy =
1 2 3 4 5 6-1-2-3-4-5-6
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
x
y
Figure 5:
(
)
xfy
=
