Determine the intervals for which the function is concave up or concave down. State the inflection points. 
$f(x)=2\sin x+3x$; $0$ < $x$ < $2\pi$

• A. Concave down: $\left(0,\pi\right)$; concave up: $\left(\pi,2\pi\right)$; Inflection pt: $\left(\pi,3\pi\right)$
• B. Concave down: $\left(0,\pi\right)$; concave up: $\left(\pi,2\pi\right)$; Inflection pt: $\left(\pi,2+3\pi\right)$
• C. Concave down: $\left(0,\frac{\pi}{2}\right)$, $\left(\pi,\frac{3\pi}{2}\right)$; concave up: $\left(\frac{\pi}{2},\pi\right)$, $\left(\frac{3\pi}{2},2\pi\right)$; Inflection pts: $\left(\frac{\pi}{2},\frac{4+3\pi}{2}\right)$, $\left(\pi,3\pi\right)$, $\left(\frac{3\pi}{2},\frac{-4+9\pi}{2}\right)$
• D. Concave up: $\left(0,2\pi\right)$; No inflection pt

Answer: (A)