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Question $18$

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$21$

Details

Consider the function $f(x)=\frac{x^2-6x5}{x3}.$

a$.$ Find the first derivative. $f^{\text{'}}(x)=\frac{x^{2}6x-23}{(x3{)}^2}$

b$.$ List any critical values. $(-3-4\sqrt[\phantom{2}]{2}),(-34\sqrt[\phantom{2}]{2})$

c$.$ Identify intervals of increase.

d$.$ Identify intervals of decrease.

e$.$ Find the second derivaitve. $f^{\text{'}\text{'}}(x)=$

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

$8.$ Based on parts b through e$,f(x)$ has a minimum of $y=$

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

when $x=$

$$

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

$$

Use the second derivative to find any inflection points.

k$.$ State any vertical asymptotes

L$.$ State any slant asymptotes. $q,$

$q,$