If $f$ is [[Continuous]] on $[a, b]$, then there exists a number $C$ in $[a, b]$ such that $f(C)$ is the average value of $f$ on the [[Range]] $[a, b]$. $\huge f(C)(b-a) = \int_{a}^b f(x)\d{x}\iff f \text{ is continuous} $ > [[The average value of a Function]]