MathDB
Problems
Contests
National and Regional Contests
Vietnam Contests
Hanoi Open Mathematics Competition
2008 Hanoi Open Mathematics Competitions
5
max P(x)- min P(x)= b-a, for all x\in [a,b] (HOMC 2008 Q5)
max P(x)- min P(x)= b-a, for all x\in [a,b] (HOMC 2008 Q5)
Source:
July 25, 2019
polynomial
algebra
Problem Statement
Find all polynomials
P
(
x
)
P(x)
P
(
x
)
of degree
1
1
1
such that
m
a
x
a
≤
x
≤
b
P
(
x
)
−
m
i
n
a
≤
x
≤
b
P
(
x
)
=
b
−
a
\underset {a\le x\le b}{max} P(x) - \underset {a\le x\le b}{min} P(x) =b-a
a
≤
x
≤
b
ma
x
P
(
x
)
−
a
≤
x
≤
b
min
P
(
x
)
=
b
−
a
,
∀
a
,
b
∈
R
\forall a,b\in R
∀
a
,
b
∈
R
where
a
<
b
a < b
a
<
b
Back to Problems
View on AoPS