Question

If $f\left(x\right)=x.e^{x(1-x)}$ then f(x) is

• A. Increasing on $[\frac{-1}{2},1]$
• B. Decreasing on R
• C. Increasing on R
• D. Decreasing on $[\frac{-1}{2},1]$

Answer 1

The correct option is A Increasing on $[\frac{-1}{2},1]$

$f^{\prime }\left(x\right)=-e^{x(1-x)}(x-1)(2x+1)$
i.e. $f^{\prime }\left(x\right)\ge 0$ when $x\in [\frac{-1}{2},1]$