CBSE Class 12 Mathematics 2026 Main Paper 65/3/2 · Q252 Marksmonotonicity
CBSE Class 12 Mathematics 2026 Main Paper 65/3/2 · Question 25 (Applications Of Derivatives)
Find where \(f(x)=x^2e^{-x}\) increases on (0,∞).
✅ Step-by-Step Solution
Final Answer: (0,2), with 2 also valid as an endpoint.
- Differentiate to obtain f′=x(2−x)e⁻ˣ.
- On the given domain x and e⁻ˣ are positive, so the sign is that of 2−x.
- The function increases up to x=2 and decreases afterward.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Differentiate to obtain f′=x(2−x)e⁻ˣ.
- [1 mark] On the given domain x and e⁻ˣ are positive, so the sign is that of 2−x.
- [0.5 marks] The function increases up to x=2 and decreases afterward.
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