The function \( f(x)=x e^{x(1-x)}, x \in \mathbb{R} \) is
(a) Increasing in \( \left(-\frac{1}{2...
The function \( f(x)=x e^{x(1-x)}, x \in \mathbb{R} \) is
(a) Increasing in \( \left(-\frac{1}{2}, 1\right) \)
(b) Decreasing in \( \left(\frac{1}{2}, 2\right) \)
(c) Increasing in \( \left(-1,-\frac{1}{2}\right) \)
(d) Decreasing in \( \left(-\frac{1}{2}, \frac{1}{2}\right) \)
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