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If f(x)=x e^(x(x-1)) , then a) f(x) is i...

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

A

increasing on`[-1//2,1]`

B

decreasing on R

C

incresing on R

D

decreasing on `[-1//2,1]`

Text Solution

Verified by Experts

The correct Answer is:
1
`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]`
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