Answer:
Option b ) 2.310
Step-by-step explanation:
Given that the function is
[tex]y = sin (x-sinx)[/tex]
For finding when the tangent is parallel to x axis, we must find the least positive value of x for which y' i.e. derivative =0
Differentiate y with respect to x using chain rule.
[tex]y' = cos(x-sinx) * (1-cosx)[/tex]
Equate this to 0
Either one factor should be zero.
[tex]cos(x-sinx)=0\\x-sinx =\frac{\pi}{2} \\[/tex]
x=2.31 satisfies this
For the other root,
[tex]1-cos x =0\\cos x =1\\x =0\\[/tex]
Since positive least value is asked we can say
x =2.310
Option b
