Consider the function $\displaystyle {f{{\left({x}\right)}}}={9}{x}+{5}{x}^{{-{1}}}$. For this function there are four important intervals: $\displaystyle {\left(-\infty,{A}\right]}$, $\displaystyle {\left[{A},{B}\right)}$,$\displaystyle {\left({B},{C}\right]}$, and $\displaystyle {\left[{C},\infty\right)}$ where $\displaystyle {A}$, and $\displaystyle {C}$ are the critical numbers and the function is not defined at $\displaystyle {B}$.
Find $\displaystyle {A}$ Preview Question 6 Part 1 of 9  
and $\displaystyle {B}$ Preview Question 6 Part 2 of 9  
and $\displaystyle {C}$ Preview Question 6 Part 3 of 9  

For each of the following open intervals, tell whether $\displaystyle {f{{\left({x}\right)}}}$ is increasing or decreasing.
$\displaystyle {\left(-\infty,{A}\right)}$: Select an answer Increasing Decreasing
$\displaystyle {\left({A},{B}\right)}$: Select an answer Increasing Decreasing
$\displaystyle {\left({B},{C}\right)}$: Select an answer Increasing Decreasing
$\displaystyle {\left({C},\infty\right)}$ Select an answer Increasing Decreasing

Note that this function has no inflection points, but we can still consider its concavity. For each of the following intervals, tell whether $\displaystyle {f{{\left({x}\right)}}}$ is concave up or concave down.
$\displaystyle {\left(-\infty,{B}\right)}$: Select an answer Concave Up Concave Down
$\displaystyle {\left({B},\infty\right)}$: Select an answer Concave Up Concave Down