Near $x = 2$, how does $f(x) = x^{2} - 4 x + 1$ behave?

Explanation

1. 01

   $f'(x) = 2 x - 4$, so $f'(2) = 0$.

2. 02

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