Consider the following function.

$f(x)=x^2-4x+3$

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

$x=$

increasing

decreasing

$($c$)$ Apply the First Derivative Test to identify all relative extrema. $($If an answer does not exist, enter DNE.$)$

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

relative maximum