Let the function
$$f ( x ) = \left\{ \begin{array} { l l l } ( x - 1 ) ^ { 2 } & \text { if } & x \leq 1 \\ ( x - 1 ) ^ { 3 } & \text { if } & x > 1 \end{array} \right.$$
a) (0.5 points) Study its continuity on $[ - 4 ; 4 ]$.\ b) (1 point) Analyze its differentiability and growth on [-4;4].\ c) (1 point) Determine whether the function $g ( x ) = f ^ { \prime } ( x )$ is defined, continuous and differentiable at $x = 1$.