Let $f(x)=x^3+3z^2-105x+23$

Sketch the function using a graphing tool and answer the following questions.

$($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 endponts in the interval? interval of increasir

$($d$)$ On what interval is f decreasing $($include the endpoing in the interval? interval of decreasing $-$

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

$($f$)$ On what interval is $f$ concawe unward $($include the endpoints in the intervalp? interval of upward concavity $=$