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).
![](https://gradesaver.s3.amazonaws.com/uploads/solution/a1c04194-ed74-40d2-ae11-05beec903098/steps_image/small_1583402009.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T000648Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=115d54b939b594c15c3fd711543e4b3a338f139b1ab2d48618937fb878204b5f)