Rolle's Theorem for Root Counting

Rolle's Theorem for Root Counting

If a differentiable function has two distinct roots in an interval, then its derivative has at least one root between them.

If:

$$f(a)=f(b)=0$$

then there exists $$c\in(a,b)$$ such that:

$$f'(c)=0$$

Usage

- Used to establish bounds on the number of roots of equations.