Compute the Clarke subdifferential of a function

Question

The Clarke subdifferential of $f(x)=|x|$ at $x=0$ is a set $[-1, 1]$, and $\{sign(x)\}$ otherwise, just like the ordinary subdifferential because of convex. Now for \begin{equation} g(x)= \begin{cases} |x|/2-x^2/4, \text { if }|x|\leq 1,\\ 1/4, \text { otherwise}, \end{cases} \end{equation} what is the Clarke subdifferential of $g(x)$? I thought the Clarke subdifferential of $g$ is given by \begin{equation} \partial g(x)= \begin{cases} \{sign(x)/2-x/2\}, \text{ if } 0<|x|\leq 1,\\ \{0\}, \text{ if } |x|>1,\\ [-1/2, 1/2], \text{ if }x=0. \end{cases} \end{equation} Is my understanding correct, particularly at $x=0$?