\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(f : \mathbb{R} \to \mathbb{C}\) be \(C^1\) with \(f(0) = 0\) and \(|f'(t)| \le M\) on \(\mathbb{R}\) for some \(M > 0\). Show that \(|f(t)| \le M |t|\) for every \(t \in \mathbb{R}\).
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