Consider the function f(x) = (e^x)*cos(x) with domain \(\mathbb{R}\). Find the range of x values in [0, 2pi] for which f is increasing, decreasing, concave up, and inflection points using interval notation and a list of x values for inflection points.
I know the roots are x = 0, pi/4. and 5pi/4
Can someone please answer? Thanks!