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CGP EDU Academic Team
Published on: August 14, 2026
The set of values of p for which all the points of extremum of the function f(x) = x 3 − 3 px 2 + 3 (p 2 − 1) x + 1 lie in the interval ( − 2, 4), is:
Text Solution
Verified by ExpertsThe correct answer is:
C
f ′ (x) = 3x 2 – 3p2x + 3p 2 – 3
= 3((x – p) 2 – 1)
= 3(x –(p + 1)) (x – (p – 1))
⇒ p – 1 > – 2 and p + 1 < 4
⇒ p > – 1 and p < 3
⇒ – 1 < p < 3
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