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Mathematics
Problem
Let
f
f
f
be a function having derivatives of all orders for
x
>
0
x > 0
x
>
0
such that
f
(
3
)
=
2
f(3) = 2
f
(
3
)
=
2
,
f
′
(
3
)
=
−
1
f'(3) = -1
f
′
(
3
)
=
−
1
,
f
′
′
(
3
)
=
6
f''(3) = 6
f
′′
(
3
)
=
6
, and
f
′
′
′
(
3
)
=
12
f'''(3) = 12
f
′′′
(
3
)
=
12
. Which of the following is the third-degree Taylor polynomial for
f
f
f
about
x
=
3
x = 3
x
=
3
?
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