Consider the following function.

$f(x)=x^2-8x+5$

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

$x=4,-11$

$1$

$($b$)$ Find the open intervals on which the function is increasing or decreasing. $($Enter your answers using interval$-$notation. If an answer does not exist, enter DNE.$)$

increasing $$

decreasing $$

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

relative minimum $(x,y)=$

DNE

$$

relative maximum $(x,y)=$