The function f(x) = x² eˣ is strictly decreasing on:
The function f(x) = x² eˣ is strictly decreasing on:
- A. (−2, 0)
- B. (−∞, −2)
- C. (0, ∞)
- D. (−∞, ∞)
Answer: A) (−2, 0)
Explanation: f'(x) = 2x eˣ + x² eˣ = eˣ x(x + 2). eˣ > 0 always. f'(x) < 0 → x(x + 2) < 0 → −2 < x < 0.
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