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The value of c in Rolle's theorem for t...

The value of `c` in Rolle's theorem for the function `f(x) = x^(3) - 3x` in the interval `[0,sqrt(3)]` is

A

`1`

B

`-1`

C

`3/2`

D

`1/3`

Text Solution

Verified by Experts

The correct Answer is:
A
`:' f'(c ) = 0` , `[:' f'(x) = 3x^(2)-3]`
`rArr 3c^(2)-3=0`
`rArr c^(2) = 3/3 = 1`
`rArr c = +- 1`, where `1 in (0, sqrt(3))`
` :. c = 1`
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Knowledge Check

  • Rolle's theorem is true for the function f(x)=x^2-4 in the interval

    A
    `[-2,0]`
    B
    `[-2,2]`
    C
    `[0,1/2]`
    D
    `[0,2]`

  • What are the values of c for which Rolle's theorem for the function f(x)=x^(3)-3x^(2)+2x in the interval [0,2] is verified?

    A
    `c=+-1`
    B
    `c=1+-1/(sqrt(3))`
    C
    `c=+-2`
    D
    None of these

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