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IMC
2018 IMC
4
4
Part of
2018 IMC
Problems
(1)
IMC 2018 P4
Source: IMC 2018 P4
7/24/2018
Find all differentiable functions
f
:
(
0
,
∞
)
→
R
f:(0,\infty) \to \mathbb{R}
f
:
(
0
,
∞
)
→
R
such that
f
(
b
)
−
f
(
a
)
=
(
b
−
a
)
f
’
(
a
b
)
for all
a
,
b
>
0.
f(b)-f(a)=(b-a)f’(\sqrt{ab}) \qquad \text{for all}\qquad a,b>0.
f
(
b
)
−
f
(
a
)
=
(
b
−
a
)
f
’
(
ab
)
for all
a
,
b
>
0.
Proposed by Orif Ibrogimov, National University of Uzbekistan
differentiable function
real analysis
imc2018