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Final Exam Review Sheet
Directions:
For all problems round to the nearest thousandths as necessary.
I.
Solve as Directed.
1.
A town’s population P is a function of time P=f(t) where t=years since 1970.
Interpret f(3)=25,000 and
.
If
is negative, what does that tell us
about the population growth rate?
2.
f(x)=4x+2, g(x)=5x1, and h(x)=5x.
Find:
a. f(2)
b. g(2)
c.
f(g(2))
d.
3.
In the graph a the
right, the marks the
origin.
a.
Find f(2)
b. ESTIMATE f’(1)
c.
Is the first derivative always positive?
negative?
neither?
Why?
d.
How about the 2
nd
derivative?
e.
Is the graph concave up or down?
4.
Your grade in this class on this test is a function of the number of hours you spend
studying.
G=f(t) where t= number of hours studying and G is percentage grade.
a.
Interpret
f(0)=35
and
f(8)=95.
b.
If you graphed this function would you anticipate the first derivative to be positive
or negative?
c.
What are the units of the first derivative?
d.
If you graphed this function would you anticipate the 2
nd
derivative
to be positive or negative?
5.
Find the equation of a line if we know…
a.
it’s slope is 2 and it goes thru the point (0,5)
b.
it goes thru (8,4)
and (3,2)
6.
Using Chart 1 at the right, find each:
a.
f(5)
b.
equation of the line
represented.
c.
d.
7.
A taxi company charges $2 plus 40 cents per mile find the charge (c) the company
charges a customer to go m miles.
8.
Chart 2 depicts the height a tshirt reaches when fired by Cocky from a t
shirt cannon.
Assume that the height (feet) it reaches is a function of
the number of seconds t after it was fired
H=f(t)
a.
Find f(3) and explain its meaning.
b.
Is f(x) concave up or down?
c.
Is the 2
nd
derivative positive or negative?
d.
What is the average rate of change between the 1
st
and 4
th
seconds?
e.
What are the units of
?
x
f(x)
2
7
5
9
8
11
11
13
x
f(x)
1
30
2
50
3
58
4
62
Chart 2
Chart 1
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Chart 3 at right shows USC average attendance (in thousands) at football games the
past few seasons.
Assume that attendance A is a function of the year t
A=f(t).
a.
Is the 1
st
derivative positive or negative?
b.
What are the units?
c. Is the 2
nd
derivative positive or negative?
d.
Is f(x) concave up or down?
e.
What is the average rate of change from 2007 –
2010?
10. The population of a city is given by the function
.
The population (P)
of the city is a function of the years t since the year 2000.
Answer each of the
following:
a.
What was the population in the year 2000?
b.
At what PERCENTAGE rate is the population growing?
c. On Jan 1, 2010 give the growth rate in people/year.
11. In the graph of f(x) at the right (Assume each square is 1
unit.):
a.
Where is the 1
st
derivative positive?
b.
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This note was uploaded on 06/15/2011 for the course MATH 122 taught by Professor Kustin during the Spring '08 term at South Carolina.
 Spring '08
 KUSTIN

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