Question

The value of c in Rolle’s theorem for the function f(x) = x³ – 3x in the interval `[0, sqrt(3)]` is ______.

Options

• 1

• – 1

• `3/2`

• `1/3`

Answer 1

The value of c in Rolle’s theorem for the function f(x) = x³ – 3x in the interval `[0, sqrt(3)]` is 1.

Explanation:

Given that: f(x) = x³ – 3x in `[0, sqrt(3)]` 

We know that if f(x) = x³ – 3x satisfies the conditions of Rolle’s Theorem in `[0, sqrt(3)]`, then 

f'(c) = 0

⇒ 3c² – 3 = 0

⇒ 3c² = 3

⇒ c² = 1

∴ c = ± 1

⇒ `1 ∈ (0, sqrt(3))`.