Name:
Math 6: Test 1
February 20, 2012
Please write neatly and clearly.
For problems 14, you do not need to show your work.
Problems 59 are partial credit; you should show your work and identify your final answer.
You may use a calculator. However, no cell phones or books may be used.
Question:
1
2
3
4
5
6
7
8
Total
Points:
25
5
15
5
10
10
15
15
100
Score:
1. (25 points) Compute the following.
(a) If
f
(
x
) = 2
x

4, then
f
0
(4) =
A. 0
B. 2
C. 3
D. 4
(b) If
f
(
x
) = 9
x
3

4
x
2
+ 2, then
f
0
(
x
) =
A. 12
x
3

6
x
+ 2
B. 9
x
3
(3
x
2
)

4
x
2
(2
x
)
C. 27
x
2

8
x
D. 9 + 3
x
2

4

2
x
+ 2
(c) If
g
(
x
) = (4
π
+
π
2
)
10
, then
g
0
(
x
) =
A. 0
B. 10(4
π
+
π
2
)
9
(4 + 2
π
)
C.
1
11
(4
π
+
π
2
)
11
D. Undefined
(d) If
h
(
x
) =
1
4
x
+
x
2
, then
h
0
(
x
) =
A.
1
4 + 2
x
B.

4
x

2

2
x

3
C.
(4
x
+
x
2
)

(4 + 2
x
)
(4
x
+
x
2
)
2
D.

(4 + 2
x
)
(4
x
+
x
2
)
2
(e) If
f
(
t
) =
p
1 +
t
2
, then
f
0
(3) =
A.
3
√
10
B.
1
2
√
10
C.
√
10
D.

505
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2. (5 points) Find the equation for the tangent line to the curve
y
=
x
2
at
x
= 4.
A.
y

8 =
x

4
B.
y

16 = 8(
x

4)
C.
y

x
2
= 2
x
(
x

4)
D.
y

16 = 2
x
(
x

4)
3. (15 points) Use the graph of
g
(
x
) to answer to following questions.
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 Spring '13
 Dr. Corbett Redden
 Math, Calculus, Absolute Zero, Celsius, Thermodynamic temperature

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