Let $f(x)=-34x-x^3.$ Find the open intervals on which $f$ is increasing $($decreasing$).$ Then determine the $x-$coordinates of all relative maxima $($minima$).$

$f$ is increasing on the intervals $(-\frac{2\sqrt[\phantom{2}]{3}}{3},\frac{2\sqrt[\phantom{2}]{3}}{3})$

$f$ is decreasing on the intervals

The relative maxima of $f$ occur at $x=\frac{2\sqrt[\phantom{2}]{3}}{3}$

The relative minima of $f$ occur at $x=-\frac{2\sqrt[\phantom{2}]{3}}{3}$

Notes: In the first two, 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 two, your answer should be a comma separated list of $x$ values or the word "none".