Published by:
CGP EDU Academic Team
Published on: August 14, 2026
(iii) f(x) = 
x 3 + 5x + 7 (iv) f(x) = sin x – m sin 2x – 
sin 3x + 2mxFind the value's of 'a' for which the f(x) = (a + 2) x 3 – 3ax 2 + 9ax – 1 decreases for all x.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Sol. f ′ (x) = 3(a + 2)x 2 – 6ax + 9a < 0
⇒ (a + 2) x 2 – 2ax + 3a < 0
∴ a + 2 < 0 4a 2 – 12a (a + 2) < 0
⇒ a < – 2 ⇒ – 2a 2 – 6a < 0
a < – 2 ⇒ a ∈ (– ∝ , –3) ∪ (0, ∞ )
∴ 
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