Chapter 3 - Applications of Differentiation - 3.2 The Mean Value Theorem - 3.2 Exercises - Page 219: 1

$1; 5$

1. $f$ is continuous on the closed interval $[0,8]$. 2. $f$ is differentiable on the open interval $(0,8)$. 3. $f(0) = 3$ and $f(8) = 3$ Therefore $f$ satisfies the three hypotheses of Rolle's Theorem. Then there is a number $c$ in $(0,8)$ so that $f'c)=0$. From the graph we find that there are two such values of $c$: $c_1=1$ $c_2=5$.