Determine for which values of x in [0,2pie] the tangent line to the graph of f(x) = (sinx) / (2+cosx) is?

Question

horizontal. Give your answers in exact form - do not give decimal approximations off of the calculator.

Answer 1

f(x) = (sinx) / (2+cosx)
dydx = [(2+cosx) cosx - sinx(-sinx)]/(2+cosx)^2
dy/dx= [2cosx +cos^2x +sin^2x]/(2+cosx)^2
dy/dx = (2cosx +1)/(2=cosx)^2
Set this = 0 getting 2 cos x +1 =0
cosx = -1/2
x = 2pi/3 and 4pi/3