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.

• A. Increasing on $(-8,\infty )$Decreasing on $(-12,-8)$Concave up on $(0,\infty )$Concave down on $(-12,0)$
• B. Increasing on $(-8,\infty )$Decreasing on $(-12,-8)$Concave up on $(-12,0)$Concave down on $(0,\infty )$
• C. Increasing on $(-12,-8)$Decreasing on $(-8,\infty )$Concave down on $(-12,\infty )$No interval of concave up
• D. Increasing on $(-12,-8)$Decreasing on $(-8,\infty )$Concave up on $(-12,\infty )$No interval of concave down

Answer: (C)