The graph of the function $f$ shown above consists of six line segments. Let $g$ be the function given by $g(x) = \int_{0}^{x} f(t)\, dt$. (a) Find $g(4)$, $g'(4)$, and $g''(4)$. (b) Does $g$ have a relative minimum, a relative maximum, or neither at $x = 1$? Justify your answer. (c) Suppose that $f$ is defined for all real numbers $x$ and is periodic with a period of length 5. The graph above shows two periods of $f$. Given that $g(5) = 2$, find $g(10)$ and write an equation for the line tangent to the graph of $g$ at $x = 108$.
The graph of the function $f$ shown above consists of six line segments. Let $g$ be the function given by $g(x) = \int_{0}^{x} f(t)\, dt$.
(a) Find $g(4)$, $g'(4)$, and $g''(4)$.
(b) Does $g$ have a relative minimum, a relative maximum, or neither at $x = 1$? Justify your answer.
(c) Suppose that $f$ is defined for all real numbers $x$ and is periodic with a period of length 5. The graph above shows two periods of $f$. Given that $g(5) = 2$, find $g(10)$ and write an equation for the line tangent to the graph of $g$ at $x = 108$.