Extreme Value Theorem

If a function $f(x)$ is continuous on a closed interval $[a,b]$, then $f(x)$ has both a Maximum and a Minimum on $[a,b]$. If $f(x)$ has an extreme value on an open interval $(a,b)$, then the extreme value occurs at a Critical Point. This theorem is sometimes also called the Weierstraß Extreme Value Theorem.