Question

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

Answer: (A)

increasing on $[-\frac{1}{2},1]$

Checking for increasing or decreasing
Obtain $f^{\prime }\left(x\right)$
$f^{\prime }\left(x\right)=e^{x(1-x)}+x{e}^{x(1-x)}\left[\right(1-x)-x],x=\frac{-1}{2},1$
Therefore, $f\left(x\right)$ is increasing in $[\frac{-1}{2},1]$