CUET · MATHS · PYQ PAPER 2025
The interval in which the function \(g(x)=x^2 e^{-x}\) is increasing is :
- A \((-\infty, \infty)\)
- B \((-2,0)\)
- C \((2, \infty)\)
- D \((0,2)\)
Answer & Solution
Correct Answer
(D) \((0,2)\)
Step-by-step Solution
Detailed explanation
\(g'(x) = (2x)e^{-x} + x^2(-e^{-x}) = xe^{-x}(2-x)\) \(g'(x) > 0 \implies xe^{-x}(2-x) > 0\) \(x(2-x) > 0 \quad (\text{since } e^{-x}>0)\) \(0 Interval: \((0,2)\)
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