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IMC
2002 IMC
2
Well-known
Well-known
Source: IMC 2002 day 1 problem 2
October 7, 2005
function
real analysis
real analysis unsolved
Problem Statement
Does there exist a continuously differentiable function
f
:
R
→
R
f : \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
such that for every
x
∈
R
x \in \mathbb{R}
x
∈
R
we have
f
(
x
)
>
0
f(x) > 0
f
(
x
)
>
0
and
f
′
(
x
)
=
f
(
f
(
x
)
)
f'(x) = f(f(x))
f
′
(
x
)
=
f
(
f
(
x
))
?
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