Question $14$

Consider the function $f(x)=\frac{x^2-7x+10}{x+2}$

a$.$ Find the first derivative. $f^{\text{'}}(x)=$

b$.$ List any critical values rounded to $2$ decimal places. $$

c$.$ Identify intervals of increase rounding to $2$ decimal places. $$

d$.$ Identify intervals of decrease rounding to $2$ decimal places.

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

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

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

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

k$.$ State any vertical asymptotes

State any slant asymptotes. $$