The graph of a function $g$ is shown.

$($a$)$ Which of the following verifies that $g$ satisfies the hypotheses of the Mean Value Theorem on the interval $[0,8]?($Select all that apply.$)$

$g$ takes only positive values on the closed interval $0,8.$

$g$ is continuous on the closed interval $0,8.$

$g$ obtains at least one maximum on the closed interval $0,8.$

$g$ obtains at least one minimum on the open interval $(0,8).$

$g$ is differentiable on the open interval $(0,8).$

$g$ is continuous on the open interval $(0,8).$

$($b$)$ Estimate the value$($s$)$ of $c$ that satisfy the conclusion of the Mean Value Theorem on the interval $[0,8].($Select all that apply.$)$

$0\mathrm{.}0$