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We can differentiate y wrt x and check its value is positive.

dy/dx is positive when x(2-x) is positive as e^{-x} is always positive.

x (2 - x) is positive if 0 < x < 2 .

Hence y is increasing in the interval (0, 2)

dy/dx is positive when x(2-x) is positive as e^{-x} is always positive.

x (2 - x) is positive if 0 < x < 2 .

Hence y is increasing in the interval (0, 2)