The complete set of values of ‘a’ for which the function f(…

Maths Differentiation and Applications of Derivatives Maxima and Minima Single Correct MCQ

Published on: August 13, 2026

The complete set of values of ‘a’ for which the function f(x) = (a + 2) x 3 – 3ax 2 + 9ax – 1 decreases for all real values of x is.

(– ∞ , – 3]

(– ∞ , 0]

[– 3, 0]

[– 3, ∞ )

Text Solution

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The correct answer is:

f ′ (x) = 3(a + 2)x 2 – 6ax + 9a ≤ 0 ∀ x ∈ R

⇒ a + 2 < 0 and D ≤ 0

⇒ a < – 2 and a ∈ ( – ∞, – 3] ∪ [0, ∞ )

⇒ a ∈ ( – ∞, – 3]

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