# 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:

$f(c)≤f(x)≤f(d)∀x∈[a,b]$