Consider the equation below. $($If an answer does not exist, enter DNE.$)$

$f(x)=x^4-50x^2+6$

$($a$)$ Find the interval on which $f$ is increasing. $($Enter your answer using interval notation.$)$

Find the interval on which $f$ is decreasing. $($Enter your answer using interval notation.$)$

$($b$)$ Find the local minimum and maximum values of $f.$

local minimum value

local maximum value

$($c$)$ Find the inflection points.

$(x,y)=(,x)(smallerx-$value$)$

$(x,y)=(,)(largerx-$value$)$

Find the interval on which $f$ is concave up$.($Enter your answer using interval notation.$)$

$[$

Find the interval on which $f$ is concave down.$($Enter your answer using interval notation.$)$