Extreme Value Theorem (EVT)

states that if a function $f$ is continuous on the closed interval $[a,b]$, then $f$ must attain a maximum and a minimum, each at least once. That is, there exist numbers $c$ and $d$ in $[a,b]$ such that:

$f(c)\le f(x)\le f(d)\forall x\in [a,b]$