Using the given graph of the function $f,$ find the following.

$($a$)$ The numbers, if any, at which $f$ has a local maximum. What are these local maximum values?

$($b$)$ The numbers, if any, at which $f$ has a local minimum. What are these local minimum values?

$($a$)$ Find the value$($s$)$ of $x$ at which $f$ has a local maximum. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.x=$

$($Type an exact answer, using $$ as needed. Use a comma to separate answers as needed.$)$

B$.$ There is no local maximum value.