(17 points)\\
Given function $f ( x ) = \ln \frac { x } { 2 - x } + a x + b ( x - 1 ) ^ { 3 }$ .\\
(1) If $b = 0$ and $f ^ { \prime } ( x ) \geqslant 0$ , find the minimum value of $a$ ;\\
(2) Prove that the curve $y = f ( x )$ is centrally symmetric;\\
(3) If $f ( x ) > - 2$ if and only if $1 < x < 2$ , find the range of $b$ .