Consider the function $f(x)=12x^5+45x^4-360x^3+4.$

$f(x)$ has inflection points at $($reading from left to right$)x=D,E,$ and $F$

where $D$ is

and $E$ is

and $F$ is

For each of the following intervals, tell whether $f(x)$ is concave up or concave down.