Consider the functions defined implicitly by the equation $y ^ { 3 } - 3 y + x = 0$ on various intervals in the real line.\\
If $x \in ( - \infty , - 2 ) \cup ( 2 , \infty )$, the equation implicitly defines a unique real valued differentiable function $y = f ( x )$.\\
If $x \in ( - 2,2 )$, the equation implicitly defines a unique real valued differentiable function $y = g ( x )$ satisfying $g ( 0 ) = 0$.
If $f ( - 10 \sqrt { 2 } ) = 2 \sqrt { 2 }$, then $f ^ { \prime \prime } ( - 10 \sqrt { 2 } ) =$\\
(A) $\frac { 4 \sqrt { 2 } } { 7 ^ { 3 } 3 ^ { 2 } }$\\
(B) $- \frac { 4 \sqrt { 2 } } { 7 ^ { 3 } 3 ^ { 2 } }$\\
(C) $\frac { 4 \sqrt { 2 } } { 7 ^ { 3 } 3 }$\\
(D) $- \frac { 4 \sqrt { 2 } } { 7 ^ { 3 } 3 }$