Q. If $f(x)$ is an even function and $f^{'}(x)$ exists, then $f^{'}(e) + f^{'}( - e)$ is
A) >0
B) = 0
C) $\geq 0$
D) <0
Explanation
(b)
Since, $f(x)$ is an even function, therefore $f^{'}(x)$ is an odd function
$ie,\ \ \ \ \ \ \ \ \ \ \ \ f^{'}( - e) = - f^{'}(e)$
$\therefore\ \ f^{'}(e) + f^{'}( - e) = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.