Villarreal, Natalie – Homework 2 – Due: Sep 4 2007, 3:00 am – Inst: Louiza Fouli
1
This
printout
should
have
12
questions.
Multiplechoice questions may continue on
the next column or page – find all choices
before answering.
The due time is Central
time.
Yes, Homework 1 is due AFTER
Homework 2.
001
(part 1 of 1) 10 points
A car first slows down, but then speeds up.
Sketch a graph of the position of the car as a
function of time.
1.
time
position
2.
time
position
3.
time
position
4.
time
position
5.
time
position
6.
time
position
correct
Explanation:
When the position of the car is plotted
against time, the slope of the graph indicates
the speed of the car, the greater the slope, the
greater the speed, and the car is stationary
when the slope is zero.
Thus of the graphs,
only
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Villarreal, Natalie – Homework 2 – Due: Sep 4 2007, 3:00 am – Inst: Louiza Fouli
2
time
position
has the given properties.
Keywords:
graphical interpretation speed,
position v. time graph
002
(part 1 of 1) 10 points
The point
P
(1
,
8
5
) lies on the graph of the
function
f
defined by
f
(
x
) =
8
x
3 + 2
x
.
By calculating the slope of the secant line
PQ
for the successive points
Q
(
x, f
(
x
)) with
x
= 1
.
1
,
x
= 1
.
01
,
x
= 1
.
001
,
x
= 1
.
0001
,
and
x
= 0
.
9
,
x
= 0
.
99
,
x
= 0
.
999
,
x
= 0
.
9999
,
estimate (to 3 decimal places) the slope of the
tangent line to the graph of
f
at
P
.
Correct answer: 0
.
96 .
Explanation:
The slope of the secant line
PQ
for general
points
P
(
a, f
(
a
)) and
Q
(
b, f
(
b
)) on the graph
of
f
is given by
rise
run
=
f
(
b
)

f
(
a
)
b

a
.
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 Fall '09
 Gualdani
 Derivative, Slope, Villarreal, average vel

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