At how many points in the open interval $(0, 3)$ is $f(x) = [x] + \lvert x - 2 \rvert$ not differentiable?

Explanation

1. 01

   $[x]$ jumps at 1 and 2, so $f$ is not even continuous there, and hence not differentiable.

2. 02

   $\lvert x - 2 \rvert$ has its corner at 2, a point already counted. So 2 points.