Consider the function on the interval (0, 2𝜋). f(x) = x/2 + cos x. Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.)

Answer 1

f'(x)=(1/2)-sin(x)

f'(x)>0 when π/6<x<5π/6,,,,f(x) increasing

f'(x)<0 when 0<x<π/6 and when 5π/6<x<2π,,,,f(x) decreasing

0 and 2π are excluded from answers since the interval given for analysis is open (0,2π)

a closed interval has notation [0,2π]