Consider the function $\displaystyle {f{{\left({x}\right)}}}={3}{x}+{4}{x}^{{-{1}}}$. For this function there are four important open 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 open intervals, tell whether $\displaystyle {f{{\left({x}\right)}}}$ is increasing (type in INC) or decreasing (type in DEC).
$\displaystyle {\left(-\infty,{A}\right)}$:
$\displaystyle {\left({A},{B}\right)}$:
$\displaystyle {\left({B},{C}\right)}$:
$\displaystyle {\left({C},\infty\right)}$: