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CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/1 · Q283 Markscritical_points

CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/1 · Question 28 (Applications Of Derivatives)

Find a,b if \(y=(ax-b)/((x-1)(x-4))\) has critical point (3,1).

✅ Step-by-Step Solution

Final Answer: a=1, b=5.
  1. The point condition gives 3a−b=−2.
  2. With D=(x−1)(x−4), D(3)=−2 and D′(3)=1. Vanishing numerator of y′ gives −2a−(3a−b)=0, so b=5a.
  3. Then −2a=−2, so a=1 and b=5.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] The point condition gives 3a−b=−2.
  • [2 marks] With D=(x−1)(x−4), D(3)=−2 and D′(3)=1. Vanishing numerator of y′ gives −2a−(3a−b)=0, so b=5a.
  • [0.5 marks] Then −2a=−2, so a=1 and b=5.

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