Consider the function $f(x)=12x^5+15x^4-240x^3+6.$

$f(x)$ 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.

$(-,D)$:

$(D,E)$: Concave $Up$

$(E,F)$: Concave Down

$(F,)$: Concave $Up$

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