Q. Select the correct statement from (a), (b), (c), (d) The function $f(x) = xe^{1 - x}$
A) Strictly increasing in the interval $\left( \frac{1}{2},\ 2 \right)$
B) Increasing in the interval $(0,\ \infty)$
C) Decreases in the interval $(0,\ 2)$
D) Strictly decreasing in the interval $(1,\ \infty)$
Explanation
(d)
Since, $f(x) = x\ e^{1 - x}$
$f^{'}(x) = - xe^{1 - x} + e^{1 - x}$
$= e^{1 - x}(1 - x)$
$\Rightarrow \ \ \ f^{'}(x) < 0,\ \ \ \forall\ (1,\ \infty)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.