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Mathematics
Problem
A function
f
f
f
is defined by
f
(
x
)
=
3
x
2
−
2
f(x)=3x^{2}-2
f
(
x
)
=
3
x
2
−
2
for all real
x
x
x
. Let
F
F
F
be an antiderivative of
f
f
f
such that
F
(
1
)
=
0
F(1)=0
F
(
1
)
=
0
. (a) Find an explicit formula for
F
(
x
)
F(x)
F
(
x
)
given
F
(
1
)
=
0
F(1)=0
F
(
1
)
=
0
. (b) Determine the exact value of
F
(
4
)
F(4)
F
(
4
)
. Show all work leading to your answer.
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