In which points is the following function differentiable (in non-distributional sense)?
$$ f(t)= t \theta(t) + (1/2t^2-t+1/2)\theta(t-1)+(t-2)\theta(t-2)$$
My solution:
\begin{align*} f'(t)&= \theta(t) + (t-1) \theta(t-1)+\theta(t-2)\\ f''(t)&= \delta(t) + \theta(t-1)+\delta(t-2) \end{align*}
However, I am not sure how I should interpret my results. A part of belives every point except $t=0,1,2$ when looking at $f(t)$. However when looking at $f'(t)$ and $f''(t)$ I think that it might be every point except $t=0,2$.
How should I interpret my $f'$ and $f''$ and will it help to solve my question?