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Mathematics
Mathematics
Problem
Let
f
f
f
be a continuous function on
[
2
,
7
]
[2,7]
[
2
,
7
]
and define
F
(
x
)
=
∫
2
x
f
(
t
)
d
t
F(x)=\int_{2}^{x} f(t)\,dt
F
(
x
)
=
∫
2
x
f
(
t
)
d
t
. For
2
<
x
<
7
2<x<7
2
<
x
<
7
, which of the following equals
F
′
(
x
)
F'(x)
F
′
(
x
)
? a)
f
′
(
x
)
f'(x)
f
′
(
x
)
b)
f
(
x
)
f(x)
f
(
x
)
c)
∫
2
x
f
′
(
t
)
d
t
\displaystyle \int_{2}^{x} f'(t)\,dt
∫
2
x
f
′
(
t
)
d
t
d)
F
(
x
)
F(x)
F
(
x
)
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