Consider the following function. Use a graphing utility to confirm your answers for parts $($a$)$ throus not exist, enter DNE.$)$

$f(x)=x^4-32x+4$

$($a$)$ Find the critical numbers of $f.($Enter your answers as a comma$-$separated list.$)$

$x=$

$($b$)$ Find the open intervals on which the function is increasing or decreasing. $($Enter your answe notation.$)$

increasing

decreasing

$($c$)$ Apply the First Derivative Test to identify all relative extrema.

relative maximum $,(x,y)=(x)$

relative minimum $,(x,y)=()$