Question

Number of points where $g(x)=|x(2 x+1)(2 x-1)|cos\,(\pi x)$ is non-differentiable is ______.

Answer 1

$|x (2 x+1)(2 x-1)|$ is non-differentiable at $x=0, \frac{-1}{2}, \frac{1}{2}$
But $cos (\pi x)=0$ for $x=\frac{-1}{2}, \frac{1}{2}$
Hence $g(x)$ is differentiable at $x=\frac{-1}{2}, \frac{1}{2}$
Therefore there is only one point of non-differentiability $x=0$