A characterization of the zero function
Source: Romanian National Olympiad, grade xi, p.1
August 23, 2019
functionreal analysis
Problem Statement
Find all differentiable functions that verify the conditions:
\text{(i)} \forall x\in\mathbb{Z} f'(x) =0 \text{(ii)} \forall x\in\mathbb{R} f'(x)=0\implies f(x)=0