Consider the following. f$($x$)=2$x$^3-3$x$^2-12$x

$($a$)$ Find the intervals on which$$f$$is increasing or decreasing. $($Enter your answers using interval notation.$)$

increasing

decreasing

$($b$)$ Find the local maximum and minimum values of$$f$.($If an answer does not exist, enter DNE.$)$

local minimum value

local maximum value

$($c$)$ Find the intervals of concavity and the inflection points. $($Enter your answers using interval notation.

concave up

concave down

inflection point