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CGP EDU Academic Team
Published on: August 11, 2026
Let ƒ(x) = (x – 3) (x – 4) (x – 5) (x – 6), then -
Text Solution
Verified by ExpertsThe correct answer is:
B
ƒ(x) = (x – 3) (x – 4) (x – 5) (x – 6)
⇒ ƒ(3) = ƒ(4) = ƒ(5) = ƒ(6) = 0
∴ by Rolle’s theorem, there exist
1 ∈ (3, 4), a 2 ∈ (4, 5) and a 3 ∈ (5, 6) such that
ƒ ′ (a i ) = 0, i = 1, 2, 3.
Since ƒ ′ (x) is a cubic polynomial therefore a 1 , a 2 , a 3 are the only roots of ƒ ′ (x) = 0.
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