Name: _____________
Test #3: Applications of Derivatives
Math 160
This is a calculus test. I need to see calculus in order to give credit. Show all work. If I don't see
calculus work, I won't give credit.
1.
f
is continuous and
a
<
b
<
c
< .
.. <
k
<
l
<
m
x
a
b
c
d
e
f
g
h
i
j
k
l
m
f
'(
x
)
–
0
+
+
+
0
+
+
+
0
–
ND
–
f
''(
x
)
+
+
+
0
–
0
+
0
–
–
–
ND
+
lim
x
−∞
f
x
=∞
lim
x
∞
f
x
=−
10
A. Where are the critical points for
f
?
B. Where does
f
have local extrema? For each one, identify it as a maximum or minimum.
C. Where are the points of inflection of
f
?
D. Sketch a graph of
f
.
E. How does
f
(
d
) compare to
f
(
h
)?
Bonus: Discuss whether or not
f
has any absolute extrema. (Under what conditions, on what intervals,
whether it's possible, etc. Be as thorough as possible.)
2. Find the limit:
lim
x
0
e
3
x
x
2
−
3
x
−
1
x
2
Bonus:
lim
x
0
+
x
p
ln
x
for
p
> 0
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For the function
g
x
=
x
x
1
When is
g
increasing?
When is
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