Question: Let f(x)=-9+10x-x3.(a) Find the interval(s) where f(x) is increasing. (Enter your answer using interval notation.)(b) Find the interval(s) where f(x) is decreasing. (Enter your answer using interval notation.)(c) Find the x-value(s) of all local maxima of f(x). (Enter your answers as a comma-separated list. If an answer does not exist, enter

Let $f(x)=-9+10x-x^3.$

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

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

$($c$)$ Find the $x-$value$($s$)$ of all local maxima of $f(x).($Enter your answers as a comma$-$separated list. If an answer does not exist, enter DNE.$)$

$x=$

$($d$)$ Find the $x-$value$($s$)$ of all local minima of $f(x).($Enter your answers as a comma$-$separated list. If an answer does not exist, enter DNE.$)$

$x=\frac{\sqrt[\phantom{2}]{30}}{3}$