Answer
$f(x)$ appears to be not differentiable at $x=0$, the tangent line being vertical.
Work Step by Step
Given $$f(x)=\sin \left(x^{1 / 3}\right), \quad a=0$$
From the following figure, at $x=0, \ \ f(x)$ appears to be not differentiable (the tangent line is vertical).
