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Mathematics
Mathematics
Problem
Let
G
(
x
)
=
∫
3
x
f
(
t
)
d
t
G(x)=\displaystyle \int_{3}^{x} f(t)\,dt
G
(
x
)
=
∫
3
x
f
(
t
)
d
t
where
f
f
f
is continuous on
R
\mathbb R
R
. Which of the following expressions equals
G
′
(
x
)
G'(x)
G
′
(
x
)
for all real
x
x
x
? a)
f
′
(
x
)
f'(x)
f
′
(
x
)
b)
−
f
(
x
)
-f(x)
−
f
(
x
)
c)
f
(
x
)
f(x)
f
(
x
)
d)
f
(
x
)
−
f
(
3
)
x
−
3
\dfrac{f(x)-f(3)}{x-3}
x
−
3
f
(
x
)
−
f
(
3
)
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