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Mathematics
Problem
A function satisfies
f
(
3
)
(
x
)
=
12
f^{(3)}(x)=12
f
(
3
)
(
x
)
=
12
for all
x
x
x
, with initial conditions
f
′
′
(
0
)
=
3
f''(0)=3
f
′′
(
0
)
=
3
,
f
′
(
0
)
=
−
2
f'(0)=-2
f
′
(
0
)
=
−
2
, and
f
(
0
)
=
1
f(0)=1
f
(
0
)
=
1
. Which expression for
f
(
x
)
f(x)
f
(
x
)
is consistent with all of the given information? a)
2
x
3
+
3
x
2
−
2
x
+
1
2x^{3}+3x^{2}-2x+1
2
x
3
+
3
x
2
−
2
x
+
1
b)
2
x
3
+
3
2
x
2
−
2
x
2x^{3}+\dfrac{3}{2}x^{2}-2x
2
x
3
+
2
3
x
2
−
2
x
c)
2
x
3
+
3
2
x
2
−
2
x
+
1
2x^{3}+\dfrac{3}{2}x^{2}-2x+1
2
x
3
+
2
3
x
2
−
2
x
+
1
d)
4
x
3
+
3
2
x
2
−
2
x
+
1
4x^{3}+\dfrac{3}{2}x^{2}-2x+1
4
x
3
+
2
3
x
2
−
2
x
+
1
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