$(1$ point$)$ Let $f(x)=7+48x-x^3.$ Find $($a$)$ the intervals on which $f$ is increasing, $($b$)$ the intervals on which $f$ is decreasing, $($c$)$ the open intervals on which $f$ is concave up$,($d$)$ the open intervals on which $f$ is concave down, and $($e$)$ the $x-$coordinates of all inflection points.

$($a$)f$ is increasing on the interval$($s$)$

$($b$)f$ is decreasing on the interval$($s$)$

$($c$)f$ is concave up on the open interval$($s$)$

$($d$)f$ is concave down on the open interval$($s$)$

$($e$)$ the $x$ coordinate$($s$)$ of the points of inflection are $0$

Notes: In the first four boxes, your answer should either be a single interval, such as $[0,1),$ a comma separated list of intervals, such as $(-$inf, $2),(3,4],$ or the word "none".

In the last box, your answer should be a comma separated list of $x$ values or the word "none".