Consider the function $\displaystyle {f{{\left({x}\right)}}}={x}^{{{2}}}{e}^{{{15}{x}}}$.
For this function there are three important 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 (type in INC) or decreasing (type in DEC).
$\displaystyle {\left(-\infty,{A}\right]}$:
$\displaystyle {\left[{A},{B}\right]}$:
$\displaystyle {\left[{B},\infty\right)}$