IMathAS-libretexts

Consider the function $\displaystyle {f{{\left({x}\right)}}}=\frac{{{x}^{{2}}-{6}{x}+{8}}}{{{x}+{3}}}$ .

Find the first derivative. $\displaystyle {f}'{\left({x}\right)}=$
List any critical values.
Identify intervals of increase.
Identify intervals of decrease.
Find the second derivaitve. $\displaystyle {f}{''}{\left({x}\right)}=$
Based on parts b through e, $\displaystyle {f{{\left({x}\right)}}}$ has a maximum of $\displaystyle {y}=$ when $\displaystyle {x}=$
Based on parts b through e, $\displaystyle {f{{\left({x}\right)}}}$ has a minimum of $\displaystyle {y}=$ when $\displaystyle {x}=$
Use the second derivative to identify intervals where $\displaystyle {f{{\left({x}\right)}}}$ is concave up.
Use the second derivative to identify intervals where $\displaystyle {f{{\left({x}\right)}}}$ is concave down.
Use the second derivative to find any inflection points.
State any vertical asymptotes.
State any slant asymptotes.