Consider the function $g$ given by $g(x)=|x-7|6.$

$($a$)$ For what $x-$value$($s$)$ is the function not differentiable?

$($b$)$ Evaluate $g^{\text{'}}(0),g^{\text{'}}(1),g^{\text{'}}(8),$ and $g^{\text{'}}(14).$