Let $\mathrm { p } ( \mathrm { x } )$ be a differentiable function such that $\mathrm { p } ( 1 ) = 2$.
If $\operatorname { Lim } _ { t \rightarrow x } \left( \frac { t ^ { 2 } p ( x ) - x ^ { 2 } p ( t ) } { x - t } \right) = 3$, then the value of $2 p ( 2 )$.