Let f (x)= {3 x, x<0; min {1+x+[x], x+2[x]}, 0 ≤ x ≤ 2; 5, x>2,} where [.] denotes greatest integer function. If α and β are the number of points,…

Let $\displaystyle \mathrm{f}(x)=\left\{\begin{array}{lc}3 x, & x<0 \\ \min \{1+x+[x], x+2[x]\}, & 0 \leq x \leq 2 \\ 5, & x>2,\end{array}\right.$ where [.] denotes greatest integer function. If $\displaystyle \alpha$ and $\displaystyle \beta$ are the number of points, where f is not continuous and is not differentiable, respectively, then $\displaystyle \alpha+\beta$ equals $\displaystyle \_\_\_\_$.