1.
Let a function g:[0,4]→Rg: [0,4] \to \mathbb{R} be defined as
g(x)={max⁡0≤t≤x{t3−6t2+9t−3},0≤x≤34−x,3<x≤4g(x) = \begin{cases} \max\limits_{0 \le t \le x} \{t^3 - 6t^2 + 9t - 3\}, & 0 \le x \le 3 \\ 4 - x, & 3 < x \le 4 \end{cases}

Then the number of points in the interval (0,4)(0, 4) where g(x)g(x) is NOT differentiable, is: