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Math 115 — Final Exam
December 17, 2010
Name:
Instructor:
Section:
1.
Do not open this exam until you are told to do so.
2.
This exam has 10 pages including this cover. There are 8 problems. Note that the problems
are not of equal diﬃculty, so you may want to skip over and return to a problem on which
you are stuck.
3.
Do not separate the pages of this exam. If they do become separated, write your name on
every page and point this out to your instructor when you hand in the exam.
4.
Please read the instructions for each individual problem carefully. One of the skills being
tested on this exam is your ability to interpret mathematical questions, so instructors will
not answer questions about exam problems during the exam.
5.
Show an appropriate amount of work (including appropriate explanation) for each problem,
so that graders can see not only your answer but how you obtained it. Include units in your
answer where that is appropriate.
6.
You may use any calculator except a TI92 (or other calculator with a full alphanumeric
keypad). However, you must show work for any calculation which we have learned how to
do in this course. You are also allowed two sides of a 3
00
×
5
00
note card.
7.
If you use graphs or tables to ﬁnd an answer, be sure to include an explanation and sketch
of the graph, and to write out the entries of the table that you use.
8.
Turn oﬀ all cell phones and pagers
, and remove all headphones.
9.
Use the techniques of calculus to solve the problems on this exam.
Problem
Points
Score
1
10
2
13
3
12
4
14
5
12
6
10
7
14
8
15
Total
100
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View Full Document Math 115 / Final (December 17, 2010)
page 2
1
. [10 points] Given below is a graph of
h
0
(
x
), the derivative of a function
h
(
x
).

1

2

3
1
2
3
x
h
¢
H
x
L
(a) On the axes below, sketch a possible graph of
h
(
x
).

1

2

3
1
2
3
x
h
H
x
L
(b) List the
x
coordinates of all inﬂection points of
h
.
(c) Give the
x
coordinate of the global minimum of
h
on [3,3].
(d) Give the
x
coordinate of the global maximum of
h
on [3,3].
Math 115 / Final (December 17, 2010)
page 3
2
. [13 points] The Uvalue of a wall of a building is a positive number related to the rate of energy
transfer through the wall. Walls with a lower Uvalue keep more heat in during the winter
than ones with a higher Uvalue. Consider a wall which consists of two materials, material A
with Uvalue
a
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This note was uploaded on 01/28/2012 for the course MATH 115 taught by Professor Blakelock during the Fall '08 term at University of Michigan.
 Fall '08
 BLAKELOCK
 Math

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