The continuous function $f$ is defined on the closed interval $- 6 \leq x \leq 12$. The graph of $f$, consisting of two semicircles and one line segment, is shown in the figure.
Let $g$ be the function defined by $g ( x ) = \int _ { 6 } ^ { x } f ( t ) d t$.
A. Find $g ^ { \prime } ( 8 )$. Give a reason for your answer.
B. Find all values of $x$ in the open interval $- 6 < x < 12$ at which the graph of $g$ has a point of inflection. Give a reason for your answer.
C. Find $g ( 12 )$ and $g ( 0 )$. Label your answers.
D. Find the value of $x$ at which $g$ attains an absolute minimum on the closed interval $- 6 \leq x \leq 12$. Justify your answer.