Today I used 2 (or more) things I learned in the class I am teaching right now. I use the general stuff everyday, but I haven't used these two theorems for my upper division work in a loooong time.
When I tell my class: "You'll need this for later..." I am not kidding. It just made my life easier.
In case you are curious: I used the Intermediate Value Theorem and the Descartes' Rule of Signs