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

Expert Answers
justaguide eNotes educator| Certified Educator

The values of x corresponding to the points at which the graph of the function f(x) = x − 2 sin x has a horizontal tangent has to be determined.

For a function f(x) the slope of the tangent at any point x = c is given by f'(c). The slope of a horizontal line is 0.

f(x) = x - 2*sin x

f'(x) = 1 - 2*cos x

1 - 2*cos x = 0

=> cos x = 1/2

=> x = `pi/3 + n*2*pi`

The values of x at which the tangent to the graph of f(x) = x - 2*sin x is horizontal are `pi/3 + n*2*pi`