Interval notation for increasing and decreasing

Question

what are the intervals for where f is increasing or decreasing

y' = 1+cos(2x)(2)

Answer 1

1 + cos(2x) > 0 for all x except x where 1 + cos(2x) = 0; cos(2x) = - 1; 2x = π(2n - 1); x = π/2(2n - 1).

So, f(x) increasing for π/2(2n - 1) < x< π/2(2n + 1), n = 0, ±1, ±2, ....