# \&lt;ey ```Exam 2
Math 1100
Name:
\&lt;ey
1 November, 2013
UID:
Instructions:
• Answer each question in the space provided.
• No calculators are allowed.
• Show all work. Answers not supported by appropriate work will not
receive credit; partial credit will be given for progress towards a solution.
Page
Points
2
16
3
8
4
27
5
24
6
25
Total:
100
Score
Math 1100
Exam 1, Page 2 of 6
For questions 1-4, assume the graph below represents
25 September, 2013
f(x).
/
10
-
0
.5
.10
1. (4 points) Point A is:
3. (4 points) At point A,
A. A relative maximum
positive
relative minimum
B. negative
C. A horizontal point of inflection
f”
is:
C. zero
D. None of the above
4. (4 points) At point B, the graph is:
2. (4 points) At point A,
f’(x)
is:
A. increasing and concave up
A. positive
ncreasing and concave down
B. negative
C. decreasing and concave up
zero
ID. decreasing and concave down
Math 1100
Exam 1, Page 3 of 6
25 September, 2013
For questions 5 and 6, assume the graph below represents
f’(x).
y
A
D
5. (4 points) Which point corresponds to a maximum of
represents f’(x))
f(x)?
(Remember the graph
Point A
B. Point B
C. Point C
D. Point D
E. None of the above
6. (4 points) At point D, the graph of
f()
A. increasing and concave up
B. increasing and concave down
decreasing and concave up
D. decreasing and concave down
(not the graph of
f’(x))
is:
Math 1100
7. Find
Exam 1, Page 4 of 6
(a) (9 points)
y
2 + 2)
ln(2x
=
d
(b) (9 points)
y = er+1
c.lI
‘-‘
K
,
•
I (x+)
—
I ()
(x+ I)
(x&divide;i
)Z.
(c) (9 points)
y
2
x
K
25 September, 2013
)&ccedil;
X)1
2
4
2.4
xy
2
3
‘C
-—)2
x
=
2y + 3x +4
Math 1100
Exam 1, Page 5 of 6
2.5 September, 2013
8. A company can produce x children’s Batman costumes at cost C(x)
revenue function from selling x Batman costumes is R(x)
16i
=
5 + 15x. The
—
(a) (18 points) How many Batmall costumes should the company produce to maximize
profit?
Rx
I
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OCt’c.4
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1—
?‘(x)
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(b) (6 points) What is the maximum possible profit for the company?
P(SO)=
Lj
5
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I
17-e r- bre
4
c.’
IViath 1100
Exam 1, Page 6 of 6
25 September. 2013
9. (25 points) •The volume of a spherical pumpkin is increasing at the rate of 4 in
/day.
3
How fast is the radius of the pumpkin increasing when the radius is 5 inches? (Note:
the volume of a sphere is given by V = ur
).
3
v
(3
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25w
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