Question

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

Answer 1

Answer:

Option b ) 2.310

Step-by-step explanation:

Given that the function is

$y = sin (x-sinx)$

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.

$y' = cos(x-sinx) * (1-cosx)$

Equate this to 0

Either one factor should be zero.

$cos(x-sinx)=0\\x-sinx =\frac{\pi}{2}$

x=2.31 satisfies this

For the other root,

$1-cos x =0\\cos x =1\\x =0$

Since positive least value is asked we can say

x =2.310

Option b