The graph of the function $f$ above consists of three line segments.
(a) Let $g$ be the function given by $g ( x ) = \int _ { - 4 } ^ { x } f ( t ) d t$.
For each of $g ( - 1 ) , g ^ { \prime } ( - 1 )$, and $g ^ { \prime \prime } ( - 1 )$, find the value or state that it does not exist.
(b) For the function $g$ defined in part (a), find the $x$-coordinate of each point of inflection of the graph of $g$ on the open interval $- 4 < x < 3$. Explain your reasoning.
(c) Let $h$ be the function given by $h ( x ) = \int _ { x } ^ { 3 } f ( t ) d t$. Find all values of $x$ in the closed interval $- 4 \leq x \leq 3$ for which $h ( x ) = 0$.
(d) For the function $h$ defined in part (c), find all intervals on which $h$ is decreasing. Explain your reasoning.