Identify the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.)

Question

Answer 1

f(x) = x + 2sinx

f'(x) = 1 + 2cosx f'(x) = 0 when cosx = -1/2. x = 2π/3, 4π/3

When 0 < x < 2π/3, f'(x) > 0. So, f is increasing

When 2π/3 < x < 4π/3, f'(x) < 0. So, f is decreasing.

When 4π/3 < x < 2π, f'(x) > 0. So, f is increasing.