Analysis in Q\mathbb{Q}

Calculus Level 3

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

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

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