The graph of the function $f$ shown above consists of two line segments. Let $g$ be the function given by $g ( x ) = \int _ { 0 } ^ { x } f ( t ) \, dt$. (a) Find $g ( - 1 ) , g ^ { \prime } ( - 1 )$, and $g ^ { \prime \prime } ( - 1 )$. (b) For what values of $x$ in the open interval $( - 2, 2 )$ is $g$ increasing? Explain your reasoning. (c) For what values of $x$ in the open interval $( - 2, 2 )$ is the graph of $g$ concave down? Explain your reasoning. (d) On the axes provided, sketch the graph of $g$ on the closed interval $[ - 2, 2 ]$.
The graph of the function $f$ shown above consists of two line segments. Let $g$ be the function given by $g ( x ) = \int _ { 0 } ^ { x } f ( t ) \, dt$.\\
(a) Find $g ( - 1 ) , g ^ { \prime } ( - 1 )$, and $g ^ { \prime \prime } ( - 1 )$.\\
(b) For what values of $x$ in the open interval $( - 2, 2 )$ is $g$ increasing? Explain your reasoning.\\
(c) For what values of $x$ in the open interval $( - 2, 2 )$ is the graph of $g$ concave down? Explain your reasoning.\\
(d) On the axes provided, sketch the graph of $g$ on the closed interval $[ - 2, 2 ]$.