Chapter 4.5, Problem 232E

For the following exercises, determine

1. intervals where f is increasing or decreasing,
2. local minima and maxima of f,
3. intervals where f is concave up and concave down, and
4. the inflection points of f. Sketch the curve, then use a calculator to compare your answer. If you cannot determine the exact answer analytically, use a calculator.

232. [T] $f\left(x\right)=x+\sin \left(2x\right)$ over $x=\left[-\frac{\pi }{2},\frac{\pi }{2}\right]$