husain (aih243) – HW01 – Gilbert – (56215)
2
5.
time
position
correct
6.
time
position
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
time
position
has the given properties.
003
10.0 points
The point
P
(1
,
4
5
) lies on the graph of the
function
f
defined by
f
(
x
) =
4
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
.
48.
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
.
For the given points
P
and
Q
these slopes are
f
(1
.
1)
−
f
(1)
0
.
1
= 0
.
461538
,
f
(1
.
01)
−
f
(1)
0
.
01
= 0
.
478088
,
f
(1
.
001)
−
f
(1)
0
.
001
= 0
.
479808
,
f
(1
.
0001)
−
f
(1)
0
.
0001
= 0
.
479981
,
and
f
(0
.
9)
−
f
(1)
−
0
.
1
= 0
.
5
,
f
(0
.
99)
−
f
(1)
−
0
.
01
= 0
.
481928
,
f
(0
.
999)
−
f
(1)
−
0
.
001
= 0
.
480192
,
f
(0
.
9999)
−
f
(1)
−
0
.
0001
= 0
.
480019
.