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Mathematics
Problem
Let
f
(
x
)
f(x)
f
(
x
)
be a polynomial of degree 3 such that
f
(
3
)
=
1
f(3)=1
f
(
3
)
=
1
,
f
′
(
3
)
=
−
1
f'(3)=-1
f
′
(
3
)
=
−
1
,
f
′
′
(
3
)
=
0
f''(3)=0
f
′′
(
3
)
=
0
, and
f
′
′
′
(
3
)
=
12
f'''(3)=12
f
′′′
(
3
)
=
12
. Then the value of
f
′
(
1
)
f'(1)
f
′
(
1
)
is (a) 12 (b) 23 (c) -13 (d) none of these
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