Answer
See graph
Work Step by Step
$f'(0) = f'(2) = f'(4) = 0\Rightarrow$ horizontal tangents at $x = 0, 2, 4$.
$f'(x)$ $\gt$ $0$ if $x<0$ or $2$ $\lt$ $x$ $\lt$ $4 \Rightarrow$ $f$ is increasing on $(-\infty,0)$ and $(2,4)$
$f'(x)$ $\lt$ $0$ if $0$ $\lt$ $x$ $\lt$ $2$ or $x$ $\gt$ $4\Rightarrow f$ is decreasing on $(0,2)$ and $(4,\infty)$
$f''(x)$ $\gt$ $0$ if $1$ $\lt$ $x$ $\lt$ $3\Rightarrow f$ is concave upward on $(1,3)$
$f''(x)$ $\lt$ $0$ if $x$ $\lt$ $1$ or $x$ $\gt$ $3\Rightarrow f$ is concave downward on $(-\infty,1)$ and $(3,\infty)$
There are inflection points when $x$ = $1$ and $3$.
