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Mathematics
Problem
Let
F
(
x
)
=
∫
0
x
(
3
t
2
−
4
t
+
1
)
d
t
.
F(x)=\int_{0}^{x} \bigl(3t^{2}-4t+1\bigr)\,dt.
F
(
x
)
=
∫
0
x
(
3
t
2
−
4
t
+
1
)
d
t
.
Answer the following. (a) Calculate
F
′
(
x
)
F'(x)
F
′
(
x
)
. (b) Evaluate
F
′
(
2
)
F'(2)
F
′
(
2
)
. (c) Determine the exact value of
F
(
2
)
F(2)
F
(
2
)
. Show all steps in your calculation.
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