\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Define \(f : \mathbb{R} \to \mathbb{R}\) by \(f(x) = x^2\) for \(x \le 0\) and \(f(x) = x\) for \(x > 0\). Determine whether \(f\) is continuous at \(0\) and whether \(f\) is differentiable at \(0\).
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