Question

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

Answer 1

Answer: 1

$|x(2x+1)(2x-1)|$ 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 $x=0$