Happy Holidays
version
Red
Math 34A Fall 2009
Prof D.A.R.Y.L.
PRINT
NAME
Tardis
Quality
Bonus
Final
no calculators
SCORE
2
74
Put final answers in boxes on this page. Show high quality work in the blue book for all answers.
Points may be awarded for this. Number your solutions in the blue book.
At the end of the exam place this page INSIDE the blue book, and then put the bluebook inside the envelope.
This student showed me their
ID and it looks like them
(1) [
I could not tell
Checker
(poor light, no ID,...) Tardis
Checker
Tardis
y
10
/6] Use the graph given to find
(a)
Log(4700)
(b)
3.710
8
y = 10x
6
4
2
(c) What is the slope of the graph
at x = 0.6
[beware scales on the axes ]
(2) [
Find
/6]
0.2
f (x) = 4x3 − 3x2 + 7x − 9
""
(b) What is the equation of the tangent
line at x = 3 ?
(c) f """ (x)
(3) [
/6] In this question
Calculate
(c)
d
dx ((5x
p
− 2)2)
d
3x
dx (7e
+ p)
2
g(x) = px + 5x + 3
g " (3) =
is a constant
0.6
0.8
1 x
y = 2x2 − 5x + 4
(a) What is the slope of the graph
at x = 2
?
(b) f (x)
(b)
/6]
"
(a) f (x)
(a)
(4) [
0.4
slope=
[answer in form y=mx+b ]
y=
(c) What value of x gives the
minimum value of y ?
x=
(5) [
/6] After t second a rocket which is flying
h(t) = 40t − 2t2
vertically straight upwards is
meters above the ground.
(a) After how many seconds is the
rocket flying upwards at
meters per second ?
20
(b) After how many seconds is the
rocket flying downwards at
8
meters per second ?
(c) What is the maximum height
above the ground of the rocket ?
seconds
seconds
meters
y
Red
(6) [
/6] A rectangular wall is 40 meters wide
and 5 meters high. Initially 20% of the wall is
covered with paint. A painter paints the rest of the wall at
the rate of 10
square meters per hour.
(a) How many hours until the
wall is completely painted?
y = f(x)
/6]
-40
-30
-10
-20
x
10
(a) For which values of
x is f(x) increasing ?
(b) How many hours until
half the wall is covered
with paint?
(b) For which values of x is
f !! (x) negative ?
(c) How many square meters
of the wall are covered in paint
after t hours of painting ?
(8) [
(7) [
(c) For which values of
x is f ! (x) = 0 ?
/6] The table shows the number of tickets to a
hours
0
1
3
6
8
10
tickets
0
60
160
250
400
520
concert sold after the number of hours shown.
All the tickets were sold in 12 hours.
(a) What was the average rate that tickets
were sold during the 3 hours starting at time 3?
(b) During which time period was
the average rate of ticket sales
from
to
greatest?
(c) What was the average rate of
ticket sales during the last 6 hours?
(10) [
/6] A rectangular field
has 2 sides made of fence and the
12
600
tickets/
hour
(c) What length of a fence side
maximizes the area of the field ?
(a) Approximately what will the
value of the land be in the year 2012?
(b) Approximately what will the value
of the land be t years after 2005 ?
/6]
At 10 am Marie leaves Marseille
driving at 62 miles per hour along the 460 mile long road
to Paris. At 1pm Jason Bourne starts driving along the same
road from Paris toward Marseille at constant speed.
Jason meets Marie at 3pm. How fast was Bourne driving?
[Jason insists that you show work ]
Speed of Jason Bourne
=
tickets/
hour
fence
stone
stone
other two made of stone; as shown.
fence
Fence costs $ 20 per meter length.
Stone costs $ 40 per meter length.
(a) Express the total cost
of the materials (fence and
stone) in terms of the
lengths of two sides of the
field.
(b) It is decided to spend a
total of $ 2000 . Express the
length of a stone side in terms
of the length of a fence side.
(9) [
miles/hour
(11) [
/8] If tickets for a concert are sold for $100 each
2000
then
sickets are sold. For every price increase of $5
40 fewer tickets are sold. Let x be the number of $5
price increases. For example, when x is 4 the tickets are
sold for $120 each.
(a) Express the price of one ticket
in terms of x
(b) Express the number of tickets
sold in terms of x.
(c) Express the total revenue
[ = amount of money obtained by
selling tickets ] in terms of x.
(d) What should x be
be to obtain the largest revenue.
[leave your answer as a fraction]
x=
(12) [
/6] The price of a certain piece of land t years after
the year 2005 is p(t). If p! (0) = 20000 dollars per year and
p(0) = 250000
dollars, then
(c) In what year (eg 2047) do you think
the value of the land will be 470000 dollars ?