For the function $f ( x ) = 3 ( x - 1 ) ^ { 2 } + 5$, define the function $F ( x )$ as $F ( x ) = \int _ { 0 } ^ { x } f ( t ) \, dt$. A differentiable function $g ( x )$ satisfies the following for all real numbers $x$:
$$F ( g ( x ) ) = \frac { 1 } { 2 } F ( x )$$
When $g ^ { \prime } ( 2 ) = p$, find the value of $30 p$. [4 points]