vu (tv2894) – Homework 21 (Section 7.4) – miner – (55096)
1
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printout
should
have
6
questions.
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001
10.0 points
Determine
f
′
(
e
) when
f
(
x
) =
x
2
(6 + (ln
x
)
3
)
.
1.
f
′
(
e
) = 15
e
2.
f
′
(
e
) = 16
e
3.
f
′
(
e
) = 13
e
4.
f
′
(
e
) = 14
e
5.
f
′
(
e
) = 17
e
correct
Explanation:
Using the Product and Power rules we see
that
f
′
(
x
) = 2
x
(6 + (ln
x
)
3
) +
3
x
2
(ln
x
)
2
x
=
x
(12 + 2(ln
x
)
3
+ 3(ln
x
)
2
)
.
At
x
=
e
, therefore,
f
′
(
e
) = 17
e
.
002
10.0 points
Use calculus to determine which one of the
following could be the graph of
f
when
f
(
x
) =
x

2 ln
parenleftBig
x

2
2
parenrightBig

6
.
1.
2.
correct
3.
4.
5.
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vu (tv2894) – Homework 21 (Section 7.4) – miner – (55096)
2
6.
Explanation:
Since the graph of
y
= ln
x
has a vertical
asymptote at
x
= 0 and ln
x
is defined only
for
x >
0, the graph of
f
will have a vertical
asymptote at
x
= 2 and will lie to the right
of this asymptote. All the given graphs have
these properties. We need, therefore, to look
at
f
′
and
f
′′
.
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 Fall '10
 Gualdini
 Calculus, Derivative, Convex function

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