\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Define \(f : \mathbb{R} \to \mathbb{R}\) by \(f(x) = x^4\) for \(x \le 0\) and \(f(x) = x^3\) for \(x > 0\). Apply T5.2 to show \(f\) is \(C^1\) on \(\mathbb{R}\).
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