Question

The function $f ( x )= xe ^{ x (1- x )}, x \in R$, 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 $\left(-\frac{1}{2}, \frac{1}{2}\right)$

Answer 1

Answer: (A)

$ f(x)=x e^{x(1-x)} $
$f^{\prime}(x)=-e^{x(1-x)}(2 x+1)(x-1)$
$f ( x )$ is increasing in $\left(-\frac{1}{2}, 1\right)$