Where does the graph have horizontal tangent lines? f(x) = (sin(2x))+x? Calc help

Find all points on the graph of the function f(x) = (sin(2x))+x at which the tangent line is horizontal.

help?

When the derivative -0
2*cos(2*x)+1=0
cos(2x)=-1/2
x=Pi*n +/- Pi/3

Tangent lines are horizontal where f '(x) = 0
f '(x) = 2cos(2x) + 1
0 = 2cos(2x) + 1
-1 = 2cos(2x)
-1/2 = cos(2x)
2x = arccos(-1/2)
2x = 2pi/3 + 2npi or 2x = 4pi/3 + 2npi for all integers n
x = pi/3 + npi or x = 2pi/3 + npi for all integers n

find the min and max points of the curve as it moves thru the x axis


chente