wei (jw35975) – HW6 – milburn – (54685)
1
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printout
should
have
15
questions.
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before answering.
001
10.0points
Find the
y
intercept of the tangent line at
the point
P
(
−
2
,f
(
−
2)) on the graph of
f
(
x
) = 4
x
2
−
3
x
+ 4
.
1.
y
intercept =
−
20
2.
y
intercept = 20
3.
y
intercept = 19
4.
y
intercept =
−
12
correct
5.
y
intercept =
−
19
6.
y
intercept = 12
Explanation:
To use the pointslope formula to determine
an equation for the tangent line we need to
know first the point
P
(
−
2
,f
(
−
2)) and the
slope
m
=
lim
h
→
0
f
(
−
2 +
h
)
−
f
(
−
2)
h
of the tangent line at
P
.
Now
f
(
−
2) = 26,
while
f
(
−
2 +
h
) = 4
h
2
−
19
h
+ 26
.
Thus
m
=
lim
h
→
0
4
h
2
−
19
h
h
=
−
19
.
By the pointslope formula, therefore, the tan
gent line at
P
has equation
y
−
26 =
−
19(
x
+ 2)
,
which after simplification becomes
y
=
−
19
x
−
12
.
Consequently, its
y
intercept =
−
12
.
002
10.0points
Find the slope of the secant line passing
through
(
−
3
, f
(
−
3))
,
(1
, f
(1))
when
f
(
x
) =
−
x
2
+ 2
x
+ 2
.
1.
slope = 4
correct
2.
slope =
15
4
3.
slope =
17
4
4.
slope =
9
2
5.
slope =
7
2
Explanation:
Since the points
(
−
3
, f
(
−
3))
,
(1
, f
(1))
lie on the secant line, the slope of that line is
given by
rise
run
=
f
(1)
−
f
(
−
3)
1
−
(
−
3)
.
Thus
slope = 4
.
003
10.0points
A Calculus student leaves the RLM build
ing and walks in a straight line to the PCL
Library. His distance from RLM after
t
min
utes is given by the graph
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wei (jw35975) – HW6 – milburn – (54685)
2
2
4
6
8
10
12
min
yards
80
160
240
320
400
What is his speed after 3 minutes, and in
what direction is he heading at that time?
1.
towards RLM at 20 yds/min
2.
away from RLM at 30 yds/min
3.
towards RLM at 40 yds/min
4.
away from RLM at 20 yds/min
5.
towards RLM at 30 yds/min
6.
away from RLM at 40 yds/min
correct
Explanation:
The graph is linear and has positive slope
on [2
,
4], so the speed of the student at time
t
= 3 coincides with the slope of the line on
[2
,
4]. Hence
speed =
240
−
160
4
−
2
=
40 yds/min
.
As the distance from RLM is increasing on
[2
,
4] the student is thus moving away from
the RLM.
004
10.0points
If
f
is a differentiable function, then
f
′
(
a
)
is given by which of the following?
I. lim
h
→
0
f
(
a
+
h
)
−
f
(
a
)
h
II. lim
x
→
a
f
(
x
)
−
f
(
a
)
x
−
a
III. lim
x
→
a
f
(
x
+
h
)
−
f
(
x
)
h
1.
I and II only
correct
2.
I and III only
3.
I only
4.
I, II, and III
5.
II only
Explanation:
Both of
f
′
(
a
) =
lim
h
→
0
f
(
a
+
h
)
−
f
(
a
)
h
and
f
′
(
a
) =
lim
x
→
a
f
(
x
)
−
f
(
a
)
x
−
a
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 Fall '11
 MILBURN
 Calculus, Derivative, Slope, lim

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