Mean Value & Rolle's Theorem

These two theorems are pretty annoying, and you'll never see them again. On the bright side, there's only like two types of problems your teacher can ask about them, so at least we won't waste too much time on them!

The Mean Value Theorem

In theory (and maybe in your teacher's lectures), the MVT is a Very Important Theorem all about instantaneous rate of change vs average rate of change, a theorem which underlies the very foundations of Calculus. But you don't care about that. You care about the one type of problem that every teacher puts on the test, and how to get it right!

Rolle's Theorem

Rolle's Theorem is just a special case of the Mean Value theorem, when the derivative happens to be zero. The one problem that every teacher asks about this theorem is slightly different than the one they always ask about the MVT, but the result is the same: you totally know what's going to be on the test!