CBSE Class 12 Mathematics 2026 Main Paper 65/4/2 · Q232 Marksmonotonicity
CBSE Class 12 Mathematics 2026 Main Paper 65/4/2 · Question 23 (Applications Of Derivatives)
Find where f(x)=x/ln x increases on (0,1)∪(1,∞).
✅ Step-by-Step Solution
Final Answer: [e,∞), with positive derivative on (e,∞).
- Differentiate to get f′=(ln x−1)/(ln x)².
- The denominator is positive on the domain. The numerator is positive only for x>e.
- Thus the increasing interval starts at e.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Differentiate to get f′=(ln x−1)/(ln x)².
- [1 mark] The denominator is positive on the domain. The numerator is positive only for x>e.
- [0.5 marks] Thus the increasing interval starts at e.
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