# Analysis in \(\mathbb{Q}\)

**Calculus**Level 3

It is a well-known theorem that if \(f:\mathbb{R}\to\mathbb{R}\) is a differentiable function such that \(f'(t)=0\) for all \(t\in\mathbb{R}\), then \(f\) is constant.

Is it true that if \(f:\mathbb{Q}\to\mathbb{Q}\) is a differentiable function such that \(f'(t)=0\) for all \(t\in\mathbb{Q}\), then \(f\) is constant?

**Notations**:

- \(\mathbb R \) denotes the set of real numbers.
- \(\mathbb Q \) denotes the set of rational numbers.