\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Show that \(f : \mathbb{R} \to \mathbb{R}\), \(f(x) = x^3\) for \(x \ge 0\) and \(f(x) = -x^3\) for \(x < 0\) (i.e. \(f(x) = |x|^3\)), is \(C^2\) on \(\mathbb{R}\) but not \(C^3\).
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