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Math 184 Group Work 2
Instructions: Please work on the following problems with your group. (This might just
be the people sitting near you in class.) These problems are meant to be a bit diFcult,
so please spend AT LEAST 15 minutes thinking about the assignment amongst your
group before coming to ask me for help. There is a page of hints at the end of the
assignment; if you have thought about a problem for AT LEAST 5 minutes and don’t
see how to do it, then take a look at the hints.
1. Find the derivatives of the following functions, using whatever rules you
like.
Remember that
d
dx
(
e
x
) =
e
x
,
d
dx
(ln
x
) =
1
x
,
d
dx
(sin
x
) = cos
x
, and
d
dx
(cos
x
) =

sin
x
.
a.
f
(
x
) = cos(
e
x
)
b.
h
(
t
) =
2
3
+
1
3
t
3
+
2
t
2
3
c.
m
(
x
) = sin(cos(
π
2
))
d.
k
(
x
) = ((
x
2
+ 1)
3
+ 2)
4
e.
q
(
z
) = sin(
z
2
+ 1) cos(
z
2
+ 1) ln(
z
2
+ 1)
1
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View Full Document 2. Suppose that you operate a lemonade stand, and that
f
(
x
) represents the
revenue in dollars which you will make in a day if you purchase
x
lemons at the
beginning of that day.
a. Explain in words what the equation
f
(200) = 50 means.
b. What sign do you think that
f
′
(
x
) will always have for this problem? Why?
What are the units of
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This note was uploaded on 11/03/2009 for the course ECON 210 taught by Professor James during the Spring '09 term at The University of British Columbia.
 Spring '09
 James

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