Existence of a Root

Existence of a Root

If $$f(x)$$ is continuous on $$[a,b]$$ and:

$$f(a)f(b)<0$$

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

$$f(c)=0$$

Terminology

- This is the Intermediate Value Theorem applied to a sign change.

Usage

- Used to prove that an equation has at least one real root in an interval.