Split a curve into separate curves at its inflection points

Choose Curve Edit > Cut > Break Curve at Inflections.
Pick a curves you want to break.

The Break curve at inflections tool highlights the inflection points on the picked curve(s) with red arrows.
Click Go.
The curve is split into multiple curves at all the inflection points.

Note
If the curve had construction history, only one of the new curves will retain the construction history.