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South Korea USCM
2018 Korea USCM
6
6
Part of
2018 Korea USCM
Problems
(1)
Easy gronwall type inequality
Source: 2018 South Korea USCM P6
8/14/2020
Suppose a continuous function
f
:
[
0
,
1
]
→
R
f:[0,1]\to\mathbb{R}
f
:
[
0
,
1
]
→
R
is differentiable on
(
0
,
1
)
(0,1)
(
0
,
1
)
and
f
(
0
)
=
1
f(0)=1
f
(
0
)
=
1
,
f
(
1
)
=
0
f(1)=0
f
(
1
)
=
0
. Then, there exists
0
<
x
0
<
1
0<x_0<1
0
<
x
0
<
1
such that
∣
f
′
(
x
0
)
∣
≥
2018
f
(
x
0
)
2018
|f'(x_0)| \geq 2018 f(x_0)^{2018}
∣
f
′
(
x
0
)
∣
≥
2018
f
(
x
0
)
2018
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