MathDB
Problems
Contests
Undergraduate contests
Vojtěch Jarník IMC
2008 VJIMC
Problem 3
f^(n+1)(x)>f^(n)(x)+c, f analytic
f^(n+1)(x)>f^(n)(x)+c, f analytic
Source: VJIMC 2008 1.3
June 16, 2021
differential equation
calculus
Problem Statement
Find all
c
∈
R
c\in\mathbb R
c
∈
R
for which there exists an infinitely differentiable function
f
:
R
→
R
f:\mathbb R\to\mathbb R
f
:
R
→
R
such that for all
n
∈
N
n\in\mathbb N
n
∈
N
and
x
∈
R
x\in\mathbb R
x
∈
R
we have
f
(
n
+
1
)
(
x
)
>
f
(
n
)
(
x
)
+
c
.
f^{(n+1)}(x)>f^{(n)}(x)+c.
f
(
n
+
1
)
(
x
)
>
f
(
n
)
(
x
)
+
c
.
Back to Problems
View on AoPS