vu (tv2894) – Homework 21 (Section 7.4) – miner – (55096)
1
This
print-out
should
have
6
questions.
Multiple-choice questions may continue on
the next column or page – find all choices
before answering.
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.
This
preview
has intentionally blurred sections.
Sign up to view the full version.
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
′′
.
This is the end of the preview.
Sign up
to
access the rest of the document.
- Fall '10
- Gualdini
- Calculus, Derivative, Convex function
-
Click to edit the document details
