Consider the function $\displaystyle {f{{\left({x}\right)}}}={x}^{{{2}}}{e}^{{{9}{x}}}$.
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 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
$\displaystyle {\left({B},\infty\right)}$ Select an answer Increasing Decreasing