University of California, Riverside
Department of Mathematics
Midterm 2
Mathematics 9A  First Year of Calculus
Sample 2
Instructions:
This exam has a total of 100 points. You have 50 minutes.
You must show all your work to receive full credit You may use any result
done in class. The points attached to each problem are indicated beside the
problem. You are not allowed to use books, notes, or calculators. Answers
should be written as
p
2
as opposed to
1
:
4142135
:::
.
1. Compute the derivative of each of the following functions. You do not
need to simplify your answers.
(a) (6 points)
f
(
x
) = (2
x
3
+ 3
x
)
4
(
x
5
3
x
3
+ 7)
2
=
3
(b) (6 points)
g
(
x
) =
sin
x
1+4
x
+
x
3
(c) (8 points)
h
(
x
) = cos
sec
1
(
x
2
+1)
3
±±
2
y
2
+ 3
xy
2
x
2
= 40
(a) (10 points) Using implicit di/erentiation, compute
dy
dx
.
(b) (10 points) Find the coordinates of each point on the curve which
has a horizontal tangent line.
3. A weight is allowed to move upwards and downwards while suspended
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 Spring '09
 Nouh
 Calculus, horizontal tangent line, Riverside Department of Mathematics

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