can any1 help?

Question

f(x)=X+2cos(x)

find points at which the tangent line is horizontal

Answer 1

f '(x)=1-2sin(x)
f '(x)=0 => horizontal
sin(x)=1/2
x=pi/6 + r(pi) where r=0,1,2,3,...

Answer 2

If the tangent line is horizontal, it has zero slope.
So, if we differentiate...f'(x)= 1-2 sin(x) and set this to zero, then sin(x)=1/2, which happens at pi/6, 2pi/3, 13pi/6 etc. To find actual point coordinates,go back to f(x) and substitute in the x value in the equation to find the y-value. For instance, for the first point, x=pi/3 and cos(x)=
(1/2)sqrt(3) so y= pi/6+sqrt(3) when x=pi/6