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.