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$Let f (x) = x e^{x (1 - x)}, then f (x) is$

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increasing on [−1/2,1]

decreasing on R

increasing on R

decreasing on [−1/2,1]

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detailed solution

Correct option is A

f′(x)=ex(1−x)+x(1−2x)ex(1−x)=1+x−2x2ex(1−x)=−(x−1)(2x+1)ex(1−x) Since ex(1−x)>0 for all x, so f′(x)>0 if and only if (x−1)(2x+1)<0 i.e. −1/2=min(1,−1/2)

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Let f(x)=xex(1−x), then f(x) is

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$Let f (x) = x e^{x (1 - x)}, then f (x) is$