Find the absolute maximum value and the absolute minimum value, if any, of the function. $($If an answer does not exist, enter DNE.$)$

$f(x)=5x-10ln(x)on\frac{1}{2},3$

Absolute maximum value: $$ at $x=($Enter your answers as a comma$-$separated list if there are multiple $x-$values.$)$

Absolute minimum value: $$ at $x=($Enter your answers as a comma$-$separated list if there are multiple $x-$values.$)$

Complete the following parts.

$($a$)$ The domain of the function $f$ is $-($Enter your answer using interval notation.$)$

$($b$)$ To determine the absolute extreme values of the function $f,$ we need the critical numbers of $---$Select$---$

$$

$($c$)$ To find these critical numbers, we need to find $-=-($Express your answer as a single fraction. Use positive exponents only.$)$

$($d$)$ These critical numbers are as follows. $($If a critical number is an endpoint of the domain, do NOT include it in your answer. Enter your answers as a comma$-$separated list. If an answer does not exist, enter DNE.$)$

$x=$

$$

$($e$)$ The Closed Interval Optimal Test $---$Select$--$be used to find the absolute maximum value and the absolute minimum value of the function.