If y=sin(x-sinx), what is the smallest positive value of x for which the tangent line is parallel to the x-axis

(a) 1.677

(b) 2.310

(c) 3.142

(d) 3.973

(e) 6.283

Option b ) 2.310

Step-by-step explanation:

Given that the function is

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.

Equate this to 0

Either one factor should be zero.

x=2.31 satisfies this

For the other root,

Since positive least value is asked we can say

x =2.310

Option b

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step-by-step explanation: