The function $f(x)=x \mathrm{e}^{x(1-x)}, x \in \mathbb{R}$, is :

Question

increasing in $\left(-\frac{1}{2}, 1\right)$

decreasing in $\left(\frac{1}{2}, 2\right)$

increasing in $\left(-1,-\frac{1}{2}\right)$

decreasing in $\left(-\frac{1}{2}, \frac{1}{2}\right)$

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