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Mathematics
Mathematics
Problem
If
f
f
f
and
g
g
g
are differentiable functions in
(
0
,
1
)
(0, 1)
(
0
,
1
)
satisfying
f
(
0
)
=
2
=
g
(
1
)
f(0) = 2 = g(1)
f
(
0
)
=
2
=
g
(
1
)
,
g
(
0
)
=
0
g(0) = 0
g
(
0
)
=
0
and
f
(
1
)
=
6
f(1) = 6
f
(
1
)
=
6
, then for some
c
∈
[
0
,
1
]
c \in [0, 1]
c
∈
[
0
,
1
]
a.
2
f
′
(
c
)
=
g
′
(
c
)
2f'(c) = g'(c)
2
f
′
(
c
)
=
g
′
(
c
)
b.
2
f
′
(
c
)
=
3
g
′
(
c
)
2f'(c) = 3g'(c)
2
f
′
(
c
)
=
3
g
′
(
c
)
c.
f
′
(
c
)
=
g
′
(
c
)
f'(c) = g'(c)
f
′
(
c
)
=
g
′
(
c
)
d.
f
′
(
c
)
=
2
g
′
(
c
)
f'(c) = 2g'(c)
f
′
(
c
)
=
2
g
′
(
c
)
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