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B
decreasing on R
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C
increasing on R
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D
decreasing on [−12,1]
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Solution
The correct option is A increasing on [−12,1] f(x)=xex(1−x) ⇒f′(x)=ex(1−x)+(1−2x)xex(1−x) =−ex(1−x)(2x2−x−1)=−ex(1−x)(2x+1)(x−1) ∴f(x) is increasing on [−12,1]