Consider the function $\displaystyle {f{{\left({x}\right)}}}={x}^{{{2}}}{e}^{{{7}{x}}}$.

$\displaystyle {f{{\left({x}\right)}}}$ has two inflection points at x = C and x = D with C < D
where C is Preview Question 6 Part 1 of 5  
and D is Preview Question 6 Part 2 of 5  

Finally for each of the following intervals, tell whether $\displaystyle {f{{\left({x}\right)}}}$ is concave up or concave down.
$\displaystyle {\left(-\infty,{C}\right)}$: Select an answer Concave Up Concave Down
$\displaystyle {\left({C},{D}\right)}$: Select an answer Concave Up Concave Down
$\displaystyle {\left({D},\infty\right)}$ Select an answer Concave Up Concave Down