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Mathematics
Mathematics
Problem
If
f
(
x
)
f(x)
f
(
x
)
is continuous function in
[
0
,
2
π
]
[0, 2\pi]
[
0
,
2
π
]
and
f
(
0
)
=
f
(
2
π
)
f(0) = f(2\pi)
f
(
0
)
=
f
(
2
π
)
, then prove that there exists a point
c
∈
(
0
,
π
)
c \in (0, \pi)
c
∈
(
0
,
π
)
such that
f
(
c
)
=
f
(
c
+
π
)
f(c) = f(c + \pi)
f
(
c
)
=
f
(
c
+
π
)
.
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