$(1$ point$)$ Let $f(x)=-x^4-7x^{3}2x6.$ Find the open intervals on which $f$ is concave up $($down$).$ Then determine the $x-$coordinates of at inflection points of $f.$

$f$ is concave up on the interval $$

$f$ is concave down on the intervals $$

The inflection points occur at $x$ : $$

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 $(-$int, $2),(3,4),$ or the word "none". In the last one, your answer should be a comma separated list of $x$ values or the word "none".

Note: You can earn partial credit on this problem.