If `f(x)=x e^(x(x-1))` , then `f(x)` is increasing on `[-1/2,1]` decreasing on `R` increasing on `R` (d) `` decreasing on `[-1/2,1]`

Options

A. increasing on`[-1//2,1]`
B. decreasing on `[-1//2,oo]`
C. incresing on R
D. decreasing on `[-1//2,oo]`

Answer

1

Explanation

`f(X) =xe^(x)(1-x)`
or `f(X) =e^(x)(1-x) +(1-2x)xe^(xe)`
`=-e^(x)(1-x)(2x^(2)-x-1)`
`=-e^(x)(1-x)(2x+1)(x-1)` ltbr Sign scheme of f(x) is as follows

Thsu g(x) is incresing in `[-1//2,1]`