Analyzing curves

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   Let $f(x) = x^{3} - 12x + 10$. Find the critical point(s) of $f$: the value(s) of $x$ where $f'(x) = 0$.

2. Warm-up

   Let $f(x) = x^{3} - 75x + 3$. Find the critical point(s) of $f$: the value(s) of $x$ where $f'(x) = 0$.

3. Warm-up

   Let $f(x) = x^{3} - 27x + 10$. Find the critical point(s) of $f$: the value(s) of $x$ where $f'(x) = 0$.

Problems shown under their original terms: Generated (template, solver-computed).