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

Question

The function f ( x )= xe x (1- x ), x ∈ R, is (A) increasing in (-(1/2), 1) (B) decreasing in ((1/2), 2) (C) increasing in (-1,-(1/2)) (D) decreasing in (-(1/2), (1/2))

Tardigrade Admin · Accepted Answer

f(x)=x ex(1-x) f prime(x)=-ex(1-x)(2 x+1)(x-1) f ( x ) is increasing in (-(1/2), 1)

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

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

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

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

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

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

Q. The function f(x)=xex(1−x),x∈R, is

increasing in (−21​,1)

decreasing in (21​,2)

increasing in (−1,−21​)

decreasing in (−21​,21​)