Discontinuity points are not at the edges of the discontinuity.

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I think I have a good idea of the cause of this artefact.

Below I limited the number of points to 51 to magnify the problem and highlighted all the points.
numberOfPoints=51&screens=3&allPoints=true

On the right, in green, I attempted to show where the "real" intersections of the parabola and the line should be.
This intersection does not lie on a point, but between two points. As a result, it creates a small shoulder on the original curve. In turn, the small shoulder creates a non zero derivative.

[veillette]

WIth the work in #208, this is working much better for the first derivative.

However, there is still some work to be done with the second derivative.

[pixelzoom]

Very nice!

[veillette]

The work on the second derivative is being tracked in #275

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Since we are tracking the work of the second derivative in #275, we can close this issue.