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Class 12 Applications Of Derivatives · Mcq Single Correct1 Marksmonotonicity

Class 12 Maths · Applications Of Derivatives · Mcq Single Correct #18

For f(x)=2sin³x−3sin²x+12sin x+5 on [0,π/2], which statement holds?

(A) Decreasing on [0,π/2]
(B) Increasing on [0,π/2]
(C) Increasing on [0,π/4], decreasing on [π/4,π/2]
(D) None of these

✅ Step-by-Step Solution

Final Answer: Option (B): Increasing on [0,π/2]

f′=6cos x[(sin x−1/2)²+7/4]>0 in the interior, so f is strictly increasing on the closed interval.

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