Q. 955.0( 2 Votes )

# The value of c in Rolle’s theorem for the function f(x) = x^{3} – 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) = x^{3} – 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

⇒ 3c^{2} – 3 = 0 [∵ f’(x) = 3x^{2} – 3 ]

⇒ c^{2} = 1

⇒ c = ±1

⇒ c = 1 ∈

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