MathDB
Problems
Contests
Undergraduate contests
Putnam
2016 Putnam
A6
Putnam 2016 A6
Putnam 2016 A6
Source:
December 4, 2016
Putnam
Putnam 2016
Putnam calculus
Putnam analysis
Problem Statement
Find the smallest constant
C
C
C
such that for every real polynomial
P
(
x
)
P(x)
P
(
x
)
of degree
3
3
3
that has a root in the interval
[
0
,
1
]
,
[0,1],
[
0
,
1
]
,
∫
0
1
∣
P
(
x
)
∣
d
x
≤
C
max
x
∈
[
0
,
1
]
∣
P
(
x
)
∣
.
\int_0^1|P(x)|\,dx\le C\max_{x\in[0,1]}|P(x)|.
∫
0
1
∣
P
(
x
)
∣
d
x
≤
C
x
∈
[
0
,
1
]
max
∣
P
(
x
)
∣.
Back to Problems
View on AoPS