Chapter 12.3, Problem 50E

a.

To determine

The intervals where the function $f\left(x\right)=e^x\cos x,\left(0\le x\le 2\pi \right)$ is increasing and where it is decreasing.

b.

To determine

The relative extrema of $f\left(x\right)=e^x\cos x,\left(0\le x\le 2\pi \right)$.

c.

To determine

The concavity of the function $f\left(x\right)=e^x\cos x,\left(0\le x\le 2\pi \right)$.

d.

To determine

The points of inflections of the function $f\left(x\right)=e^x\cos x,\left(0\le x\le 2\pi \right)$.