Just needed to clarify a 'graph the derivative' question and the answer.

The graph on the left below is f(x) and the one on the right is f'(x), as labelled.

I remember learning that derivatives don't exist at endpoints (hoping some could also explain why this is so) so you use a open end circle, but in the answer they've used a close end circle and I don't understand why they've done it like that.