Near $x = 2$, how does $f(x) = x^{3} - 3 x$ behave?

Explanation

1. 01

   $f'(x) = 3 x^{2} - 3$, so $f'(2) = 9$.

2. 02

   A positive derivative means the function is rising there, a negative one falling, and 0 a turning or flat point.