\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Find the critical points of \(f : \mathbb{R} \to \mathbb{R}\), \(f(x) = x^3 - 3 x\). Show by direct comparison of values (no monotonicity theorem) that \(x = -1\) is a local maximum and \(x = 1\) is a local minimum. (A full classification by the sign of \(f'\) is deferred to the monotonicity section.)
Capture an image of your work. AI teacher feedback takes approximately 10 seconds.