Question $15$

$\frac{0}{1}$ pt $100$

Let $f(x)=x^{3}9x^2-48x1.$

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

For the next parts of the problem, used closed interval notation to enter your answers:

$($c$)$On what interval is $f$ increasing $($or more specifically, non$-$decreasing$)?$ interval of increasing $-$

$($d$)[$On what interval is $f$ decreasing $($or more specifically, non$-$increasing$)?$ interval of decreasing $.$

$($e$)2$ On what interval is $f$ concave dowward $($include the endooints in the interval$)?$ interval of downward concavity $-$

$($f$)$On what interval is $f$ concave upward $($include the endpoints in the interval$)?$ interval of upward concavity $-$

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