Consider the function $f\left(x\right)=-2x\sqrt{x+12}$. Determine intervals where $f$ is increasing and decreasing, and the intervals on which the curve is concave up and concave down.

Increasing on $(-8,\infty )$

Decreasing on $(-12,-8)$

Concave up on $(0,\infty )$

Concave down on $(-12,0)$

Increasing on $(-8,\infty)$

Decreasing on $\left(-12,-8\right)$

Concave up on $(-12,0)$

Concave down on $(0,\infty )$

Increasing on $(-12,-8)$

Decreasing on $\left(-8,\infty\right)$

Concave down on $\left(-12,\infty\right)$

No interval of concave up

Increasing on $(-12,-8)$

Decreasing on $\left(-8,\infty\right)$

Concave up on $\left(-12,\infty\right)$

No interval of concave down