For the function below, find $(A)f^{\text{'}}(x),(B)$ the partition numbers for $f^{\text{'}},(C)$ the critical numbers of $f.$

$f(x)=\frac{1}{x+7}$

$($A$)f^{\text{'}}(x)=-\frac{1}{(x+7{)}^2}$

$($B$)$ Find the partition numbers for $f^{\text{'}}.$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.$ The partition number$($s$)$ is$/$are $x=($Use a comma to separate answers as needed.$)$

B$.$ There are no partition numbers.

$($C$)$ Find the critical numbers of f $.$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.$ The critical number$($s$)$ is$/$are $x=($Use a comma to separate answers as needed.$)$

B$.$ There are no critical numbers.