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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`
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