Answer
$ f(x)$ appears to be not differentiable at $x=0$ (the tangent line does not exist at this point).
Work Step by Step
Given $$f(x)=|\sin x|, \quad a=0$$
From the following figure, $f(x)$ has a sharp corner at $x=0$. $f(x)$ appears to be not differentiable (the tangent line does not exist at this point).
