Let $\mathrm{f}\left(\mathrm{x}\right)=\left\{\begin{array}{l}\left|4{\mathrm{x}}^2-8\mathrm{x}+5\right|,\text{ if }8{\mathrm{x}}^2-6\mathrm{x}+1\ge 0\\ \left[4{\mathrm{x}}^2-8\mathrm{x}+5\right],\text{ if }8{\mathrm{x}}^2-6\mathrm{x}+1<0\end{array}\right.$ where [$\mathrm{\alpha }$] denotes the greatest integer less than or equal to $\mathrm{\alpha }$. Then the number of points in R where f is not differentiable is _______.

$$\begin{gathered} 8x^2-6x+1=\left(2x-1\right)\left(4x-1\right). \\ 8x^2-6x+1\ge 0\Rightarrow x\le \frac{1}{4},x\ge \frac{1}{2} and 8x^2-6x+1<0\Rightarrow \frac{1}{4}<x<\frac{1}{2} \\ 4x^2-8x+5>0 for all x \sin ce descriminant<0 \end{gathered}$$
$f\left(x\right)=$$\left\{\begin{array}{ll}4x^2-8x+5& if x\le \frac{1}{4},x\ge \frac{1}{2}\\ 3& if\frac{1}{4}<x<x_1\\ 2& if x_1<x<\frac{1}{2}\end{array}\right.$

Therefore f(x) is not differentiable  at $x= \frac{1}{4},{\mathrm{x}}_1,\frac{1}{2}$