NCERT Class 12 · Ch 6 Exercise 6.2 · Q19
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.2 Question 19
On which interval is y=x²e^(−x) increasing?
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: D: (0,2).
- y′=e^(−x)(2x−x²)=e^(−x)x(2−x).
- The exponential is positive; the product x(2−x) is positive exactly on (0,2).
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