Intermediate Value Theorem

An existence theorem that shows something can exist. It does not find where the roots are, but it can tell you it exists

Definition

1. $f$ is a continuous function on the closed interval $[a,b]$
2. $N$ is any number between $f(a)$ and $(b)$

• $\therefore$ $\exists c\in (a,b)$ such that $f(c)=N$. Of course, there can be multiple values of $c$ that satisfy the $N$ in the theorem.

Proof

• IVT Proof

IVT Questions

• IVT c squared Question