Consider the following function. f$($x$)=2$x$312$x$2+18$x $7$ Find the derivative. f $($x$)=$ Find any critical numbers of the function. $($Enter your answer as a comma$-$separated list. If any answer does not exist, enter DNE$)$ x $=$ Find the interval$($s$)$ on which f is increasing. $($Enter your answer using interval notation.$)$ Find the interval$($s$)$ on which f is decreasing. $($Enter your answer using interval notation.$)$ Find the local minimum and maximum value of f$.$ local minimum value$$ local maximum value$$