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Mathematics
Problem
Let
f
f
f
be continuous on
R
\mathbb R
R
, and let
g
g
g
be differentiable with
g
(
1
)
=
0
g(1)=0
g
(
1
)
=
0
and
g
′
(
1
)
=
3
g'(1)=3
g
′
(
1
)
=
3
. Define
F
(
x
)
=
∫
0
g
(
x
)
f
(
t
)
d
t
.
F(x)=\int_{0}^{g(x)} f(t)\,dt.
F
(
x
)
=
∫
0
g
(
x
)
f
(
t
)
d
t
.
Which of the following equals
F
′
(
1
)
F'(1)
F
′
(
1
)
? a)
f
(
g
(
1
)
)
f\bigl(g(1)\bigr)
f
(
g
(
1
)
)
b)
f
(
1
)
g
′
(
1
)
f(1)\,g'(1)
f
(
1
)
g
′
(
1
)
c)
f
(
g
(
1
)
)
g
′
(
1
)
f\bigl(g(1)\bigr)\,g'(1)
f
(
g
(
1
)
)
g
′
(
1
)
d)
f
(
1
)
f(1)
f
(
1
)
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