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9
2024 Team Problem 9
2024 Team Problem 9
Source:
April 23, 2024
team
Problem Statement
Suppose we have a cubic polynomial
p
(
x
)
p(x)
p
(
x
)
such that
p
(
0
)
=
0
,
p
(
1
)
=
1
,
p(0)=0,p(1)=1,
p
(
0
)
=
0
,
p
(
1
)
=
1
,
and
p
(
x
)
≤
x
p(x)\leq \sqrt x
p
(
x
)
≤
x
for
0
≤
x
≤
1.
0\leq x \leq 1.
0
≤
x
≤
1.
Suppose
p
(
0.5
)
p(0.5)
p
(
0.5
)
is maximized. What is the sum of
p
(
0.25
)
+
p
(
0.75
)
?
p(0.25)+p(0.75)?
p
(
0.25
)
+
p
(
0.75
)?
Proposed by Ishin Shah
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