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Mathematics
Mathematics
Problem
On the interval
[
0
,
π
]
[0,\pi]
[
0
,
π
]
, the function
p
(
x
)
=
sin
(
2
x
)
p(x)=\sin(2x)
p
(
x
)
=
sin
(
2
x
)
satisfies
p
(
0
)
=
p
(
π
)
p(0)=p(\pi)
p
(
0
)
=
p
(
π
)
. How many distinct numbers
c
c
c
in
(
0
,
π
)
(0,\pi)
(
0
,
π
)
satisfy
p
′
(
c
)
=
0
p'(c)=0
p
′
(
c
)
=
0
? a)
1
1
1
b)
2
2
2
c)
3
3
3
d)
Infinitely many
\text{Infinitely many}
Infinitely many
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