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VJIMC 2019 P2 Category II

Source: VJIMC 2019

March 30, 2019

real analysisfunctional equationVJIMC2019VJIMCVojtech JarnikAnnual Vojtech Jarnic

Problem Statement

Find all twice differentiable functions

f : \mathbb{R} \to \mathbb{R}

such that

f''(x) \cos(f(x))\geq(f'(x))^2 \sin(f(x))

for every

x\in \mathbb{R}

.
Proposed by Orif Ibrogimov (Czech Technical University of Prague), Karim Rakhimov (University of Pisa)