Question

f(x)=x+2sinx

Answer 1

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

Answer 2

I know the answer is (2n+1)π ± π/3 because that's in the back of the book but I need to know how I reach that answer

Answer 3

horizontal tangent lines have a slope of 0
f'(x) gives the slope of the tangent line
set f'(x) equal to 0 and solve for x

Answer 4

well yeah i did that and I came up with 2π/3 and 4π/3 for x but I'm not sure how I get from that step to the answer they put in the back of the book. It's probably some really simply algebra that my mind is going blank on.

Answer 5

looks good, just add 2*pi*n to both the values since cosine is a periodic function
4pi/3+2*pi*n = (2n+1)pi+pi/3
2pi/3+2*pi*n = (2n+1)pi-pi/3