For the function $f(x)=x^3-12x+13,$ find all intervals where the function is incressing: $f$ is increasing on $($Give your answar as an inforval or a list of inforvals, a$.$g$.,(-$Infinity.

Simiarty, find al intervals where the function is decreasing: $f$ is deornasing on $($Gim your answer as an interval or a itst of intervals, e$.$g$.,(-$infinity,$8)$ or $(1,5),(7,10).)$

Finaly, find all critical points in the graph of $f(x)$

critical points: $x=$

$($Enter your $x-$vaiues as a comma$-$spparatod kist, or none if thene are no critical points.$)$

Note: You can eam partial credit on this problam.