Theorem: Intermediate Value Theorem

• If f is continuous on a closed interval [a, b] and d is any number between f(a) and f(b). Then there exists a number c in the open interval (a, b) such that f(c) = d.

Proof:

With the work we have done so far this proof is easy. In fact, the easiest proof is an application of Bolzano's theorem, and is left as an exercise.