Consider the function $\displaystyle {f{{\left({x}\right)}}}=-{2}{x}^{{3}}+{39}{x}^{{2}}-{180}{x}+{8}$. For this function there are three important open intervals: $\displaystyle {\left(-\infty,{A}\right)}$, $\displaystyle {\left({A},{B}\right)}$, and $\displaystyle {\left({B},\infty\right)}$ where $\displaystyle {A}$ and $\displaystyle {B}$ are the critical numbers.
Find $\displaystyle {A}$ Preview Question 6 Part 1 of 5  
and $\displaystyle {B}$ Preview Question 6 Part 2 of 5  

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