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5
IMC 2020 Problem 5
IMC 2020 Problem 5
Source: IMC 2020
July 28, 2020
IMC
calculus
differential equation
Inequality
function
IMC 2020
Problem Statement
Find all twice continuously differentiable functions
f
:
R
→
(
0
,
∞
)
f: \mathbb{R} \to (0, \infty)
f
:
R
→
(
0
,
∞
)
satisfying
f
′
′
(
x
)
f
(
x
)
≥
2
f
′
(
x
)
2
.
f''(x)f(x) \ge 2f'(x)^2.
f
′′
(
x
)
f
(
x
)
≥
2
f
′
(
x
)
2
.
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