The graph of the function $f$, consisting of three line segments, is given above. Let $g ( x ) = \int _ { 1 } ^ { x } f ( t ) \, dt$. (a) Compute $g ( 4 )$ and $g ( - 2 )$. (b) Find the instantaneous rate of change of $g$, with respect to $x$, at $x = 1$. (c) Find the absolute minimum value of $g$ on the closed interval $[ - 2, 4 ]$. Justify your answer. (d) The second derivative of $g$ is not defined at $x = 1$ and $x = 2$. How many of these values are $x$-coordinates of points of inflection of the graph of $g$ ? Justify your answer.
The graph of the function $f$, consisting of three line segments, is given above. Let $g ( x ) = \int _ { 1 } ^ { x } f ( t ) \, dt$.\\
(a) Compute $g ( 4 )$ and $g ( - 2 )$.\\
(b) Find the instantaneous rate of change of $g$, with respect to $x$, at $x = 1$.\\
(c) Find the absolute minimum value of $g$ on the closed interval $[ - 2, 4 ]$. Justify your answer.\\
(d) The second derivative of $g$ is not defined at $x = 1$ and $x = 2$. How many of these values are $x$-coordinates of points of inflection of the graph of $g$ ? Justify your answer.