CBSE Class 12 Mathematics 2026 Main Paper 65/4/3 · Q232 Marksmonotonicity
CBSE Class 12 Mathematics 2026 Main Paper 65/4/3 · Question 23 (Applications Of Derivatives)
Find the intervals where f(x)=x/3+3/x increases, for x≠0.
✅ Step-by-Step Solution
Final Answer: Increasing on (−∞,−3] and [3,∞), with positive derivative in the interiors.
- Differentiate to get f′=(x²−9)/(3x²).
- The denominator is positive and the numerator is positive exactly for |x|>3.
- The two increasing intervals extend to the turning points −3 and 3.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Differentiate to get f′=(x²−9)/(3x²).
- [1 mark] The denominator is positive and the numerator is positive exactly for |x|>3.
- [0.5 marks] The two increasing intervals extend to the turning points −3 and 3.
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