Answer
$f$ satisfies the hypotheses of Rolle's Theorem on the interval $[0,8]$.
$f'(c) = 0$ when $c = 1$ or $c = 5$
Work Step by Step
1. We can see that $f$ is continuous on the closed interval $[0,8]$
2. $f$ is a smooth curve with no sharp points so $f$ is differentiable on the open interval $(0,8)$
3. $f(0) = f(8) = 3$
Therefore, according to Rolle's Theorem, there is a number c in $(0,8)$ such that $f'(c) = 0$
We can see that the slope of the graph at $x=1$ is 0. Then $f'(1) = 0$
We can see that the slope of the graph at $x=5$ is 0. Then $f'(5) = 0$
$f$ satisfies the hypotheses of Rolle's Theorem on the interval $[0,8]$.
$f'(c) = 0$ when $c = 1$ or $c = 5$
