Values of x

Question

Here is a question in the textbook that I don't know how to do for my test!

Determine all values of x for which the tangent to f(x)=x-sin2x is horizontal.

Answer 1

derivative = slope = zero when tangent is horizontal

f = x -sin2x

f' = 1 -2cos2x = 0

cos2x = 1/2

2x = 60 or -60 degrees + 360n where n = any integer

, x = 30 or -30 degrees + 180n where n = any integer