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Romanian National Olympiad 2024 - Grade 11 - Problem 1

Source: Romanian National Olympiad 2024 - Grade 11 - Problem 1

April 4, 2024

functionreal analysis

Problem Statement

Let

I \subset \mathbb{R}

be an open interval and

f:I \to \mathbb{R}

a twice differentiable function such that

f(x)f''(x)=0,

for any

x \in I.

Prove that

f''(x)=0,

for any

x \in I.