Let $f(x)=\frac{x^4-162x^2}{11}$

$($a$)$ Use the definition of a derivative or the derivative rules to find

$f^{\text{'}}(x)=$

$$

$($b$)$ Use the definition of a derivative or the derivative rules to find

$f^{\text{'}\text{'}}(x)=$

$($c$)$ On what interval is $f$ increasing $($include the endooints in the interval$)?$ interval of increasing $=$

$($d$)$ On what interval is $f$ decreasing $($include the endnoints in the interval$)?$

interval of decreasing $=$

$($e$)$ On what interval is $f$ concave downward $($include the endpoints in the interval$)?$ interval of concave downward $=$

$($f$)$ On what interval is $f$ concave upward $($include the endpoints in the interval$)?$ interval of concave upward $=(-3\sqrt[\phantom{2}]{3},3\sqrt[\phantom{2}]{3})$

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