The figure above shows the graph of the piecewise-linear function $f$. For $- 4 \leq x \leq 12$, the function $g$ is defined by $g ( x ) = \int _ { 2 } ^ { x } f ( t ) \, d t$. (a) Does $g$ have a relative minimum, a relative maximum, or neither at $x = 10$ ? Justify your answer. (b) Does the graph of $g$ have a point of inflection at $x = 4$ ? Justify your answer. (c) Find the absolute minimum value and the absolute maximum value of $g$ on the interval $- 4 \leq x \leq 12$. Justify your answers. (d) For $- 4 \leq x \leq 12$, find all intervals for which $g ( x ) \leq 0$.
The figure above shows the graph of the piecewise-linear function $f$. For $- 4 \leq x \leq 12$, the function $g$ is defined by $g ( x ) = \int _ { 2 } ^ { x } f ( t ) \, d t$.\\
(a) Does $g$ have a relative minimum, a relative maximum, or neither at $x = 10$ ? Justify your answer.\\
(b) Does the graph of $g$ have a point of inflection at $x = 4$ ? Justify your answer.\\
(c) Find the absolute minimum value and the absolute maximum value of $g$ on the interval $- 4 \leq x \leq 12$. Justify your answers.\\
(d) For $- 4 \leq x \leq 12$, find all intervals for which $g ( x ) \leq 0$.