For what values of x does the graph of f(x)=x+2sinx have a horizontal tangent?

Answer 1

f'(x) = 1 + 2cosx
= 0 for a horizontal tangent , (slope=0)

2cosx = -1
cosx = -1/2

x must be in quadrants II or III
and I know that cos π/3 = +1/2

x = π-π/3 or x = π + π/3
x = 2π/3 or x = 4π/3 , for 0 ≤ x ≤ 2π