Let $f(x)=ln(x^2+36)$

$($a$)$ Find the relative maximum and relative minimum values, if any, of the function. $($Enter your answers as a comma$-$separated list. If an answer does not exist, enter DNE.$)$

Relative maximum value$($s$)$:

Relative minimum value$($s$)$:

Complete the following parts.

$(1)$ The domain of the function $f$ is $-($Enter your answer using interval notation.$)$

$(2)$ To determine the relative maximum and relative minimum values of the function $f,$ we need the critical numbers of $---$Selact$---$

$(3)$ To find these critical numbers, we need to find $-$Select$---$ hat$(v)=-($Express your answer as a single fraction. Use positive exponents only.$)$

$(4)$ These critical numbers are as follows. $($Enter your answers as a comma$-$separated list. If an answer does not exist, enter DNE.$)$

$q,$

$x=$

$$

$($b$)$ Find the inflection point$($s$),$ if any, of the function. $($Order your answers from smallest to largest $x.$ If an answer does not exist, enter DNE.$)$

Complete the following parts.

$(1)$ To determine the inflection point$($s$)$ of the function $f,$ we use the $---$Select$--$

$(2)$ To determine the inflection point$($s$)$ of the function $f,$ we need the critical numbers of $---$Select$---$

$($Express your answer as a single fraction. Use positive exponents only.$)$

$(3)$ To find these critical numbers, we need to find

$(4)$ These critical numbers are as follows. $($Enter your answers as a comma$-$separated list. If an answer does not exist, enter DNE.$)$