Determine the intervals for which the function is concave up or concave down. State the inflection points.
$f(x)=4\ln(3x^2)$

• A. Concave down: $\left(-\infty,0\right)$; Concave up: $\left(0,\infty\right)$; Inflection pt: $\left(0,0\right)$
• B. Concave down: $\left(-\infty,0\right)$ & $\left(0,\infty\right)$; No inflection pt
• C. Concave up: $\left(-\infty,0\right)$; Concave down: $\left(0,\infty\right)$; Inflection pt: $\left(0,0\right)$
• D. Concave up: $\left(-\infty,0\right)$; Concave down: $\left(0,\infty\right)$; No inflection pt