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Values of c of Rolle's theorem for f(x)=...

Values of c of Rolle's theorem for `f(x)=sin x-sin 2x` on `[0,pi]`

A

`cos^(-1)((1+sqrt(3))/8)`

B

`cos^(-1)((1+sqrt(35))/8)`

C

`cos^(-1)((1-sqrt(38))/8)`

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
A
Given `f(x)=sinx-sin2x` on `[0,pi]`
`f'(x)=cos x-2cos 2x=cosx-[2cos^(2)x-1]`
`:.f'(x)=cosx-4cos^(2)x+2`
Consider `f'(c)=0implies4cos^(2)c-cosc-2=0`
`:.cos c=(1+-sqrt(33))/8`
`impliesc=cos(-1)((1+sqrt(3))/8)`
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Knowledge Check

  • Find the value of c in Rolle's theorem for the function f (x) = cos 2x on [0,pi] is

    A
    `pi/4`
    B
    `pi/2`
    C
    `pi/6`
    D
    `pi/3`

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