The function f ( x )= xe x ^ x (1- x ) , x R, is - Vidyadip

MCQ

The function $f ( x )= xe x ^{ x (1- x )}, x \in R$, is

✓
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

Correct option: A.

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

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

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