Consider the following. $($If an answer does not exist, enter DNE.$)$

$f(x)=2x^3-15x^{2}36x-2$

$($a$)$ Find the interval$($s$)$ on which $f$ is increasing. $($Enter your answer using interval notation.$)$

$$

$($b$)$ Find the interval$($s$)$ on which $f$ is decreasing. $($Enter your answer using interval notation.$)$

$$

$($c$)$ Find the local minimum and maximum value of $f.$

local minimum value $$

local maximum value $$