Consider the function $\displaystyle {f{{\left({x}\right)}}}={2}{x}+{3}{x}^{{-{1}}}$. 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 7  
and $\displaystyle {B}$ Preview Question 6 Part 2 of 7  
and $\displaystyle {C}$ Preview Question 6 Part 3 of 7  

For each of the following intervals, tell whether $\displaystyle {f{{\left({x}\right)}}}$ is increasing (type in INC) or decreasing (type in DEC).
$\displaystyle {\left(-\infty,{A}\right]}$:
$\displaystyle {\left[{A},{B}\right)}$:
$\displaystyle {\left({B},{C}\right]}$:
$\displaystyle {\left[{C},\infty\right)}$