Q$.$ pts$)$ Let $f$ be a function whose derivative is given as $f^{\text{'}}(x)=\frac{x{e}^{\frac{1}{x}}(x^2-4{)}^3}{(x-1{)}^3}.$

$($a$)$ Find the domain of $f^{\text{'}}.$

$($b$)$ Find all critical points of $f.$

$($c$)$ Classify the critical points of $f$ as local maximum, local minimum or neither.