If f(x)=xex(x−1), then f(x) is

f(x)=xex(1−x)or     f′(x)=ex(1−x)+(1−2x)xex(1−x)        =−ex(1−x)2x2−x−1=−ex(1−x)(2x+1)(x−1)Sign scheme of f '(x) is as follows: Thus, g(x) is increasing in [-½,1].