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Darboux's Theorem: An Introduction

This video is an introduction to Darboux's theorem from real analysis, which states that any function that is the derivative of another function must have the intermediate value property. We go over some motivation and prerequisite knowledge, as well as a corollary of this theorem. Note: at 30:37, I mentioned going over the proof of this theorem. That was my original plan for this video, but only after the last recording did I realize this video was much longer than I planned for, so I decided it would be best to leave the proof for another video. 0:00 Motivation 4:15 Example where f' is discontinuous 14:24 Remarks about the example and Darboux's theorem 23:32 Primer on the intermediate value property 28:42 Statement of Darboux's theorem 31:12 A corollary of Darboux's theorem 34:40 Proof of corollary