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22.
We show that the righthand derivative at 1 does not exist.
lim
h
→
0
1
}
f
(1
1
h
h
)
2
f
(1)
}5
lim
h
→
0
1
}
3(1
1
h
h
)
2
(1)
3
}
5
lim
h
→
0
1
}
2
1
h
3
h
} 5
lim
h
→
0
1
1
}
2
h
}
1
3
2
5‘
23.
lim
h
→
0
1
}
f
(0
1
h
h
)
2
f
(0)
}5
lim
h
→
0
1
}
ˇ
h
w
2
h
ˇ
0
w
}5
lim
h
→
0
1
}
ˇ
h
h
w
}
5
lim
h
→
0
1
}
ˇ
1
h
w
}5‘
Thus, the righthand derivative at 0 does not exist.
24.
Two parabolas are parallel if they have the same derivative
at every value of
x
. This means that their tangent lines are
parallel at each value of
x
.
Two such parabolas are given by
y
5
x
2
and
y
5
x
2
1
4.
They are graphed below.
[
2
4, 4] by [
2
5, 20]
The parabolas are “everywhere equidistant,” as long as the
distance between them is always measured along a vertical
line.
25.
For
x
.2
1, the graph of
y
5
f
(
x
) must lie on a line of
slope
2
2 that passes through (0,
2
1):
y
52
2
x
2
1. Then
y
(
2
1)
52
2(
2
1)
2
1
5
1, so for
x
,2
1, the graph of
y
5
f
(
x
) must lie on a line of slope 1 that passes through
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.
 Spring '08
 GERMAN
 Derivative, Limits

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