The function $f(x)=x \cdot e^{x(1-x)}$ is

• Correct answer
  A

  increasing in $\left[-\frac{1}{2}, 1\right]$
• B

  decreasing in $\left[-\frac{1}{2}, 1\right]$
• C

  increasing in $\mathbb{R}$
• D

  decreasing in $\mathbb{R}$

Hence, the correct answer is option: 'A'.