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

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

A

`a=-11`

B

`b=-6`

C

`a=6`

D

`a=11`

Text Solution

Verified by Experts

The correct Answer is:
D
Since f(x) satisfies conditions of Rolll's theorem.
`:. f(1)=f(3)`
`rArr 2-6+a+b+=27-54+3a+b rArr =11`
Now, `f'(x)=3x^(2)-12x+a=3x^(2)-12x+11`
Clearly, `f'((2sqrt(3)+1)/(sqrt(3)))=0` Hence, a=11
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