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Find the difference between the greatest and least values of the function `f(x) =sin 2x-x" on "[-(pi)/(2), (pi)/(2)]`.

A

`pi`

B

`(sqrt(3) -(pi)/(3))`

C

`(sqrt(3))/(2) +(pi)/(3)`

D

`-(sqrt(3))/(2) +(2pi)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
`y=sin 2x -x`
`y.=2 cos 2x -1=0`
`rArr cos 2x =(1)/(2)`
`rArr 2x= pm (pi)/(3)`
`rArr x= pm (pi)/(6)`
`y((pi)/(6)) = (sqrt(3))/(2) -(pi)/(6)`
`y(-(pi)/(6)) = -(sqrt(3))/(6) +(pi)/(6)`
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