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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
Given `f(x)=x^(3)-3x`
`implies f'(x)=3x^(2)-3`
By Rolle's theorem `f'(c)=0`
`implies3c^(3)-3=0impliesc^(2)=3/3=1`
`impliesc=+-1` [where `1 epsion(0,sqrt(3))`]
`implies c=1`
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