Consider the quartic polynomial $\displaystyle {f{{\left({x}\right)}}}=$ $\displaystyle -\frac{{x}^{{4}}}{{2}}+{2}{x}^{{3}}+{9}{x}^{{2}}$.
$\displaystyle {f{{\left({x}\right)}}}$ has two inflection points at $\displaystyle {x}={C}$ and $\displaystyle {x}={D}$ with $\displaystyle {C}\leq{D}$
where $\displaystyle {C}=$
and $\displaystyle {D}=$

For each of the following intervals, determine 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


The graph of $\displaystyle {f{{\left({x}\right)}}}$ shown below will help you determine whether your answers are reasonable, but you need to use Calculus to determine the exact answers.