\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Show, via the \(DL_1\) characterization, that \(f : \mathbb{R} \to \mathbb{R}\), \(f(x) = x^3\), is differentiable at every \(a \in \mathbb{R}\) and recover \(f'(a) = 3 a^2\). (Hint: expand \((a + h)^3\).)
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