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.