It’s a pretty dumb theorem stating the obvious… As per.

Informally, if a continuous differentiable function starts and ends at the same over a given range, then there’s at least one critical point.

Rolle's Theorem

If:

  • Differentiable on a range
  • Starts and ends at the same (I.E. )
  • There must be a such that (I.E. It’s a extrema…)

Further Applications:

With this, we’re able to generalise more freely to The Mean Value Theorem.