MATH 140
Take-Home Quiz # 2. Part E
To be submitted as a single .pdf file via the drop-box at ANGEL
1
INSTRUCTIONS
Write legibly and neatly the solutions to the following problems in the order in which they
appear in the assignment.
The solutions must be numbered the same way as the questions.
On top of the first page, write your name and section.
No credit will be given for correct answers not supported by work. Show all steps of your
work.
You have two options for submitting your work – a hard copy or an electronic file. The
electronic submission is the preferred form.
Submitting electronically:
Scan the pages with the solutions. Create a single multi-page
pdf file of reasonable size (no more than 3 GB). The size of the file can be reduced if you
choose gray instead of color option for the scan, and a smaller resolution. Use your name in
the name of the file, for example, John_Smith.pdf. Submit the file via the Take-Home Quiz
#2 Part E drop box at ANGEL by 9:00 am on Monday, November 2. If you are unable to
create a multipage pdf file of reasonable size and of good quality, it’s better that you
submit a hard copy instead.
Submitting a hard copy:
Use a copy machine to make a good quality copy of your solutions
and turn it in at the beginning of the class period on Monday, November 2.
There will be one point penalty if your submission does not follow the above requirements.
On the other hand, there will be one bonus point for submitting electronically.
1. Consider the function
1
2
2
x
x
x
f
. Determine if it satisfies the hypotheses of Rolle’s Theorem
on the interval
2
,
0
. If yes, find the numbers
c
that satisfy the conclusion of the theorem. If no,
explain why.
2. Consider the function
2
3
x
x
f
. Determine if it satisfies the hypotheses of the Mean
Value Theorem on the interval
6
,
1
. If yes, find the numbers
c
that satisfy the conclusion of the
theorem. If no, explain why.
3-6.
Determine the domain and the equations of all asymptotes of the following functions.
3.
9
2
5
2
2
3
x
x
x
x
f
4.
8
2
30
5
5
2
2
x
x
x
x
g
5.
16
2
x
x
x
h
6.
x
x
x
x
x
j
4
6
3
3
3
2

MATH 140
Take-Home Quiz # 2. Part E
To be submitted as a single .pdf file via the drop-box at ANGEL
2
7. The graph below shows the function
f
(
x
), defined for all real numbers.
(a)
List the
x-
coordinates of the local maximums of
f
(
x
).
(b)
List the
x-
coordinates of the local minimums of
f
(
x
).
(c)
List the intervals, on which
f
(
x
) is increasing.
(d)
List the intervals, on which
f
(
x
) is decreasing.
(e)
List the intervals, on which
f
(
x
) is concave downward.
(f)
List the intervals, on which
f
(
x
) is concave upward.
(g)
List the
x-
coordinates of the inflection points of
f
(
x
).
y
x
-6
-5
-4
-3
-2
-1
0
5
4
3
2
1
-1
-2
-3
-4
1
2
3
4
5
6