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CGP EDU Academic Team
Published on: August 12, 2026
Let f(x) = x 3 + 6x 2 + px + 2. If the largest possible interval, in which f(x) is a decreasing function, is (–3, –1), then p equals
Text Solution
Verified by ExpertsThe correct answer is:
A
f ′ (x) = 3x 2 + 12x + p < 0
f(x) is decreasing in (– 3, – 1)
⇒ f ′ (x) ≤ 0 in (– 3, – 1)
⇒ 3 × (–3) 2 + 12 × (–3) + p ≤ 0 and
3 × (–1) 2 + 12 × (–1) + p ≤ 0 ⇒ p ≤ 9 ⇒ p = 9
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