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CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/3 · Q283 Marksabsolute_extrema

CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/3 · Question 28 (Applications Of Derivatives)

Find the product of maximum and minimum values of cos x−(1/2)cos 2x on [0,π/2].

✅ Step-by-Step Solution

Final Answer: 3/8.
  1. Let u=cos x, so u∈[0,1]. The expression becomes 1/2+u−u².
  2. Its maximum is 3/4 at u=1/2 by completing the square, and both endpoints give 1/2, the minimum.
  3. The product is (3/4)(1/2)=3/8.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Let u=cos x, so u∈[0,1]. The expression becomes 1/2+u−u².
  • [2 marks] Its maximum is 3/4 at u=1/2 by completing the square, and both endpoints give 1/2, the minimum.
  • [0.5 marks] The product is (3/4)(1/2)=3/8.

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All Questions in CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/3

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