Darboux function

Summary

A Darboux function is a real function on an interval that has the intermediate value property. It never skips a value between two of its values. Every continuous function on an interval is a Darboux function by the intermediate value theorem. By Darboux's theorem, every derivative is a Darboux function too, even when it is not continuous. So the class of Darboux functions is much larger than the class of continuous functions.