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CGP EDU Academic Team
Published on: August 13, 2026
Let ƒ(x) = x 3 + ax 2 + bx + 5 sin 2 x be an increasing function in the set of real numbers R. Then a and b satisfy the condition -
Text Solution
Verified by ExpertsThe correct answer is:
C
We have ƒ(x) = x 3 + ax 2 + bx + 5 sin 2 x
⇒ ƒ ′ (x) = 3x 2 + 2ax + b + 5 sin 2x
ƒ (x) is an increasing function
∴ ƒ ′ (x) > 0 ⇒ 3x 2 + 2ax + b + 5 sin 2x > 0,
sin 2x < 1
∴ 0 < 3x 2 + 2ax + b + 5 sin 2x < 3x 2 + 2ax + b + 5
⇒ 3x 2 + 2ax + b + 5 > 0
⇒ 4a 2 – 4.3 (b + 5) > 0
⇒ a 2 – 3b – 15 < 0.
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