Determine the intervals on which the following function is concave up or concave down. Identify any inflection points.

$f(x)=2x^4+16x^3+48x^2-x-6$

Determine the intervals on which the following function is concave up or concave down. Select the correct choice and, if necessary, fill in the answer box$($es$)$ to complete your choice.

A$.$ The function is concave up on $$ and concave down on $($Simplify your answers. Type your answers in interval notation. Use a comma to separate answers as needed.$)$

B$.$ The function is concave down on $$ and the function is never concave up$.$

$($Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.$)$

C$.$ The function is concave up on $(-,-2),(-2,)$ and the function is never concave down.

$($Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.$)$

D$.$ The function is never concave up nor concave down.

Locate any inflection points of f $.$ Select the correct choice and, if necessary, fill in the answer box to complete your choice.

A$.$ An inflection point occurs at $x=-2.$

$$

$($Use a comma to separate answers as needed.$)$

B$.$ There are no inflection points for $f.$