Consider the function $\displaystyle {f{{\left({x}\right)}}}={12}{x}^{{5}}+{45}{x}^{{4}}-{360}{x}^{{3}}+{7}$.

$\displaystyle {f{{\left({x}\right)}}}$ has inflection points at (reading from left to right) x = D, E, and F

where D is Preview Question 6 Part 1 of 7  
and E is Preview Question 6 Part 2 of 7  
and F is Preview Question 6 Part 3 of 7  

For each of the following intervals, tell whether $\displaystyle {f{{\left({x}\right)}}}$ is concave up or concave down.

$\displaystyle {\left(-\infty,{D}\right)}$: Select an answer Concave Up Concave Down
$\displaystyle {\left({D},{E}\right)}$: Select an answer Concave Up Concave Down
$\displaystyle {\left({E},{F}\right)}$: Select an answer Concave Up Concave Down
$\displaystyle {\left({F},\infty\right)}$: Select an answer Concave Up Concave Down