Check if the function $f\left(x\right)=2x\sqrt{6-x}$ satisfies the conditions of the following theorem on its domain. If it does, identify the location and the value of the absolute extremum guaranteed by the theorem.
Theorem: Suppose $f$ is continuous on an interval $I$ that contains exactly one local extremum at $c$. If a local maximum occurs at $c$, then $f\left(c\right)$ is the absolute maximum of $f$ on $I$. If a local minimum occurs at $c$, then $f\left(c\right)$ is the absolute minimum of $f$ on $I$.