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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`
Solution
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))`.
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