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Mathematics
Problem
Let
F
′
(
x
)
=
3
x
2
−
4
x
+
1
F'(x)=3x^2-4x+1
F
′
(
x
)
=
3
x
2
−
4
x
+
1
. Determine whether there exists a function
F
F
F
satisfying both
F
(
1
)
=
2
F(1)=2
F
(
1
)
=
2
and
F
(
2
)
=
10
F(2)=10
F
(
2
)
=
10
. If such a function exists, state the required constant of integration
C
C
C
; if not, state why it is impossible.
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