Suppose I have a function:
$$ p=3\cdot (x(t))^{2/3} $$
In that function, $x$ depends on time $t$, but do we say in our notation that $p$ depends on $t$, or just on $x$? Specifically, we require that $p$ is globally Lipschitz with respect to $x$ and piecewise continuous with respect to $t$. Question: in the above function, is there any point of checking if $p$ is piecewise continuous with respect to $t$? Or is that needed only for function that are explicitly dependent on $t$, such that $g=3\cdot (x(t))^{2/3}\cdot t^2$?
Thank you!