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?

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