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If the function f(x)=x^(3)-6x^(2)+ax+b s...

If the function `f(x)=x^(3)-6x^(2)+ax+b` satisfies Rolle's theorem in the interval `[1,3]` and `f'((sqrt(3)+1)/(sqrt(3)))=0`, then

A

`a=-11`

B

`a=-6`

C

`a=6`

D

`a=11`

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x)=x^(3)-6x^(2)+ax+b`
On differentiating w.r.t `x` we get
`f'(x)=3x^(2)-12x+a`
By the definitions of Rolle's theorem,
`f'(c)=0`
`impliesf'(2+1/(sqrt(3)))=0`
`3(2+1/(sqrt(3)))^(2)-12(2+1/(sqrt(3)))+a=0`
`3(4+1/3+4/(sqrt(3)))-12(2+1/(sqrt(3)))+a=0`
`implies12+1+4sqrt(3)-24-4sqrt(3)+a=0`
`impliesa=11`
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