Consider the function $f(x)=\frac{x^2-5x+6}{x-4}.$

$a.$ Find the first derivative. $f^{\text{'}}(x)=\frac{x^2-8x+14}{(x-4{)}^2}{f}^{\text{'}\text{'}}(x)=$

$f.$ Based $on$ parts $b$ through $e,f(x)$ has a maximum $ofy=$

when $x=$

$g.$ Based $on$ parts $b$ through $e,f(x)$ has a minimum $ofy=$

when $x=$

$|.$

$h.$ Use the second derivative $to$ identify intervals where $f(x)is$ concave $up.$

$i.$ Use the second derivative $to$ identify intervals where $f(x)is$ concave down.

$j.$ Use the second derivative $to$ find any inflection points.

$k.$ State any vertical asymptotes.

I. State any slant asymptotes $\{use$ long division $of$ polynomials$\}.y=x-1$