Determine the inflection points and intervals of concavity for the function $f\left(x\right)=3\sin x+2x^2$, $-2\pi \le x\le \pi$.

• A. Inflection point: $x=0$Concave up on $[-2\pi ,\pi ]$
• B. Inflection point: NoneConcave up on $\(\left\]\lbrack\)-2\(\pi\),\(\pi\[\right\]\rbrack\)$
• C. Inflection point: NoneConcave up on $(0,\pi )$Concave down on $(-2\pi ,0)$
• D. Inflection point: NoneConcave up on $(-2\pi ,0)$Concave down on $(0,\pi )$

Answer: (B)