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CGP EDU Academic Team
Published on: August 12, 2026
Let f(x) = (x 2 − 1) n (x 2 + x + 1). f(x) has local extremum at x = 1 if
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a,c,d)f ′ (x) = (x – 1) n – 1 (x + 1) n – 1 [2(n + 1)x 3 + (2n + 1)x 2 + 2(n – 1)x – 1]
At x = 1 2(n + 1)x 3 + (2n + 1)x 2 + 2 (n – 1)x – 1 ≠ 0
for n ∈ N
∴ n – 1 must be odd
⇒ n is even
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