If you are talking about the vertical lines from the stationary points, he was only drawing lines to indicate where the graph of the derivative will cross the x-axis. I think he will show this in the next part. Also, horizontal lines have a slope of 0, not vertical lines.
Notability. Why I like it better than OneNote? You can connect it to your Dropbox Gdrive or iCloud account and make it so that it automatically converts your notes into a PDF and store it on your cloud storage. Let’s say you make a change to your notes, the PDF is updated with these changes automatically when you exit that notebook. It used to be Free. Don’t know if it’s still the case.