handa (nh5757) – Definition of a derivative – bormashenko – (54880)
1
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15
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001
10.0points
Find the slope of the secant line passing
through the points
(1
, f
(1))
,
(1 +
h, f
(1 +
h
))
when
f
(
x
) = 2
x
2

2
x
+ 1
.
1.
slope = 2
h
+ 2
2.
slope = 2
h

2
3.
slope = 2
h
+ 6
4.
slope = 4
h

6
5.
slope = 4
h

2
6.
slope = 4
h
+ 6
002
10.0points
Find an equation for the tangent line at the
point
P
(

1
,f
(

1)) on the graph of
f
(
x
) = 4
x
2

2
x
+ 3
.
1.
y
+ 10
x
+ 7 = 0
2.
y

10
x

1 = 0
3.
y
+ 10
x

7 = 0
4.
y

10
x
+ 1 = 0
5.
y

10
x
+ 7 = 0
6.
y
+ 10
x
+ 1 = 0
003
10.0points
Find an expression for the slope of the se
cant line through the points
P
(6
,h
(6)) and
Q
(
x,h
(
x
)) on the graph of
y
=
h
(
x
).
1.
slope =
h
(
x
)

h
(6)
x

6
2.
slope =
h
(6) +
h
(
x
)
6 +
x
3.
slope =
h
(
x
) +
h
(6)
6

x
4.
slope =
h
(
x
)

h
(6)
6 +
x
5.
slope =
h
(6)

h
(
x
)
x

6
004
10.0points
For which of the following functions
f
and
corresponding numbers
a
is the limit
lim
h
→
0
(1 +
h
)
3

1
h
the value of
f
′
(
a
)?
1.
f
(
x
) =
x
3
, a
= 3
2.
f
(
x
) =
x
3
, a
= 0
3.
f
(
x
) = (
x

1)
3
, a
= 1
4.
f
(
x
) = (
x
+ 1)
3
, a
= 3
5.
f
(
x
) = (
x
+ 1)
3
, a
= 1
6.
f
(
x
) =
x
3
, a
= 1
005
10.0points
If a construction worker drops a wrench
from the top of a building 375 feet high the
wrench will be
s
(
t
) =

16
t
2
+ 375
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handa (nh5757) – Definition of a derivative – bormashenko – (54880)
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 Spring '10
 Gualdini
 Derivative, Slope, lim

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