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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 – fnd all choices
be±ore answering.
The due time is Central
time.
Yes, Homework 1 is due AFTER
Homework 2.
001
(part 1 o± 1) 10 points
A car frst slows down, but then speeds up.
Sketch a graph o± the position o± the car as a
±unction o± time.
1.
time
position
2.
time
position
3.
time
position
4.
time
position
5.
time
position
6.
time
position
correct
Explanation:
When the position o± the car is plotted
against time, the slope o± the graph indicates
the speed o± the car, the greater the slope, the
greater the speed, and the car is stationary
when the slope is zero.
Thus o± the graphs,
only
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View Full Document 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
de±ned by
f
(
x
) =
8
x
3 + 2
x
.
By calculating the slope of the secant line
P Q
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
P Q
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
.
For the given points
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This note was uploaded on 04/15/2011 for the course MATH 408K taught by Professor Gualdani during the Fall '09 term at University of Texas at Austin.
 Fall '09
 Gualdani

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