The function $f$ is differentiable on the closed interval $[-6, 5]$ and satisfies $f(-2) = 7$. The graph of $f'$, the derivative of $f$, consists of a semicircle and three line segments, as shown in the figure. (a) Find the values of $f(-6)$ and $f(5)$. (b) On what intervals is $f$ increasing? Justify your answer. (c) Find the absolute minimum value of $f$ on the closed interval $[-6, 5]$. Justify your answer. (d) For each of $f''(-5)$ and $f''(3)$, find the value or explain why it does not exist.
The function $f$ is differentiable on the closed interval $[-6, 5]$ and satisfies $f(-2) = 7$. The graph of $f'$, the derivative of $f$, consists of a semicircle and three line segments, as shown in the figure.\\
(a) Find the values of $f(-6)$ and $f(5)$.\\
(b) On what intervals is $f$ increasing? Justify your answer.\\
(c) Find the absolute minimum value of $f$ on the closed interval $[-6, 5]$. Justify your answer.\\
(d) For each of $f''(-5)$ and $f''(3)$, find the value or explain why it does not exist.