Answer
See graph
Work Step by Step
$f'(5)$ = $0\Rightarrow$ horizontal tangents at $x$ = $5$
$f'(x)$ $\gt$ $0$ if $x$ $\gt$ $5\Rightarrow f$ is increasing on $(5,\infty)$
$f'(x)$ $\lt$ $0$ if $x$ $\lt$ $5\Rightarrow f$ is decreasing on $(-\infty,5)$
$f''(x)$ $\lt$ $0$ when $x$ $\lt$ $2$ or $x$ $\gt$ $8\Rightarrow f$ is concave downward on $(-\infty,2)\cup(8,\infty)$
$f''(x)$ $\gt$ $0$ for $2$ $\lt$ $x$ $\lt$ $8\Rightarrow f$ is concave upward on $(2,8)$
$f''(2)$ = $0$, $f''(8)$ = $0\Rightarrow$ there are inflection points when $x$ = $2$ and $x$ = $8$.
