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It is a well-known theorem that if f:R→Rf:\mathbb{R}\to\mathbb{R}f:R→R is a differentiable function such that f′(t)=0f'(t)=0f′(t)=0 for all t∈Rt\in\mathbb{R}t∈R, then fff is constant.
Is it true that if f:Q→Qf:\mathbb{Q}\to\mathbb{Q}f:Q→Q is a differentiable function such that f′(t)=0f'(t)=0f′(t)=0 for all t∈Qt\in\mathbb{Q}t∈Q, then fff is constant?
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