Q. For the function $f(x) = xe^{x}$the point
A) $x = 0\$is a maximum
B) $x = 0\$is a minimum
C) $x = - 1$is a maximum
D) $x = - 1\ is\ a\$minimum
Explanation
(d)
Given, $f(x) = xe^{x}$
$\Rightarrow \ \ \ \ \ \ f^{'}(x) = e^{x} + xe^{x}$
$\Rightarrow \ \ \ \ \ f^{''}(x) = e^{x} + xe^{x} + e^{x} = 2e^{x} + xe^{x}$
For maxima or minima, put $f^{'}(x) = 0$
$\Rightarrow \ \ \ \ \ e^{x}(1 + x) = 0$
$\Rightarrow \ \ \ \ x = - 1$
At $x = - 1,\ \ \ f^{''}(x) > 0$
$\therefore At\ x = - 1,\ \ f(x)$ is minimum.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.