Q. 955.0( 2 Votes )

The value of c in Rolle’s theorem for the function f(x) = x3 – 3x in the interval
A. 1

B. –1

C.

D.

Answer :

Rolle’s Theorem states that, Let f : [a, b] R be continuous on [a, b] and differentiable on (a, b), such that f(a) = f(b), where a and b are some real numbers.Then there exists some c in (a, b) such that f’(c) = 0.


We have, f(x) = x3 – 3x


Since, f(x) is a polynomial function it is continuous on and differentiable on



Now, as per Rolle’s Theorem, there exists at least one c , such that


f’(c) = 0


3c2 – 3 = 0 [ f’(x) = 3x2 – 3 ]


c2 = 1


c = ±1


c = 1

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