The interval in which y = x2 e–x is increasing is ______.

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The interval in which y = x2 e–x is increasing is (0, 2). Explanation: x2 - e-x dy/dx = 2xe^-x - x^2 e^-x = xe-x (2 - x) If f'(x) = 0 xe-x (2 - x) = 0 x = 0, 2 x = 0 and x = 2 divide the real line into intervals (- infty, 0), (0, 2) and (2, infty). Thus, (- infty, -1) and (1, infty) represent the intervals. The function y is continuously increasing in the interval (0, 2). Interval (- $\infty$, 0) (0, 2) (2, $\infty$ ) Sign of x -ve +ve +ve sign of (2 - x) +ve +ve -ve sign of e-x +ve +ve +ve sign of f' (x) -ve +ve -ve

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