For the given piece-wise function, we would need to draw an open circle at the point (0, 0).
Where we should draw an open circle?
Open circles are used to mark limits or endpoints, such that these don't belong to the function.
An example is f(x) = 4 for x < 3
Then at x = 3, we need to draw an open circle, because x = 3 does not belong to the domain.
In this case, we have the piece-wise function:
f(x) = -x x < 0.
f'(x) = 1 x ≥ 0
So, f'(0) = 1, because x = 0 belongs to the domain of the second part.
Then, we need to draw an open circle at the point (0, 0), which is what we got when we evaluate the first part in x = 0.
f(0) = -0 = 0 ⇒ (0, 0)
The open circle must be drawn at the point (0, 0) (and we will have a closed circle at the point (0, 1)).
If you want to learn more about piece-wise functions, you can read:
https://brainly.com/question/3628123
