Find the linearization $L(x,y,z)$ of the function $f(x,y,z)=xz-6yz+6$ at $P_0(3,3,3).$ Then find an upper bound for the magnitude of the error in the approximation $f(x,y,z)$~~$L(x,y,z)$ over the region $R$:$|x-3|0\mathrm{.}05,|y-3|0\mathrm{.}05,|z-3|0\mathrm{.}01.$

The linearization of $f(x,y,z)$ at $P_0(3,3,3)$ is $L(x,y,z)=3x-18y-15z+51.$

The magnitude of the error is $|E|$

$($Round to four decimal places as needed.$)$