CUET · MATHS · PYQ PAPER 2025
The interval, on which the function \(f(x)=x^2 e^{-x}\) is increasing, is equal to:
- A \((-\infty, \infty)\)
- B \((-\infty, 2) \cup(2, \infty)\)
- C \((-2,0)\)
- D \((0,2)\)
Answer & Solution
Correct Answer
(D) \((0,2)\)
Step-by-step Solution
Detailed explanation
\(f'(x) = 2xe^{-x} - x^2e^{-x} = xe^{-x}(2-x)\) \(xe^{-x}(2-x) = 0 \implies x=0\) or \(x=2\) Test interval \((0,2)\): \(f'(1) = 1 \cdot e^{-1} (2-1) = e^{-1} > 0\) The function is increasing on \((0,2)\).
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