Let $g(x)=2\sqrt[\phantom{2}]{x}3$ for $x0.$ Complete parts $($a$)$ through $($d$)$ below.

a$.$ Find the average rate of change of $g(x)$ with respect to $x$ over the intervals $1,2$

$1,1,5,$ and $1,1h.$

The average rate of change over the interval $1,2$ is $$

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