The number of points, at which the function f(x)= max {6 x, 2+3 x^2}+|x-1| cos |x^2-1/4|, x ∈(-π, π), is not differentiable, is ____.

The number of points, at which the function $\displaystyle f(x)=\max \left\{6 x, 2+3 x^2\right\}+|x-1| \cos \left|x^2-\frac{1}{4}\right|, x \in(-\pi, \pi)$, is not differentiable, is $\displaystyle \_\_\_\_$.