Chapter 4.5, Problem 237E

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.

237. $f\left(x\right)=\sin \left(x\right)e^x$ over $x=\left[-\pi ,\pi \right]$