\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Carry out a complete study of \(f(x) = x^3 - 3 x\) on \(\mathbb{R}\):
  1. determine the monotonicity intervals from the sign of \(f'\);
  2. determine the convexity intervals from the sign of \(f''\);
  3. identify the inflection point.

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