Answer
See graph
Work Step by Step
$f(0)$ = $f'(0)$ = $0\Rightarrow$ the graph of $f$ passes through the origin and has a horizontal tangent there
$f'(2)$ = $f'(4)$ = $f'(6)$ = $0\Rightarrow$ horizontal tangents at $x$ = $2,4,6$
$f'(x)$ $\gt$ $0$ if $0$ $\lt$ $x$ $\lt$ $2$ or $4$ $\lt$ $x$ $\lt$ $6\Rightarrow f$ increasing on $(0,2)\cup(4,6)$
$f'(x)$ $\lt$ $0$ if $2$ $\lt$ $x$ $\lt$ $4$ or $x$ $\gt$ $6\Rightarrow f$ decreasing on $(2,4)\cup(6,\infty)$
$f''(x)$ $\gt$ $0$ if $0$ $\lt$ $x$ $\lt$ $1$ or $3$ $\lt$ $x$ $\lt$ $5\Rightarrow f$ is concave upward on $(0,1)\cup(3,5)$
$f''(x)$ $\lt$ $0$ if $1$ $\lt$ $x$ $\lt$ $3$ or $x$ $\gt$ $5\Rightarrow f$ is concave downward on $(1,3)\cup(5,\infty)$
$f(-x)$ = $f(x)\Rightarrow f$ is even and the graph is symmetric about the $y$-axis