Q. If $f(x) = 2x^{6} + 3x^{4} + 4x^{2}$, then $f^{'}(x)$ is
A) Even function
B) An odd function
C) Neither even nor odd
D) None of these
Explanation
(b)
Given, $f(x) = 2x^{6} + 3x^{4} + 4x^{2}$
Now, $f( - x) = 2( - x)^{6} + 3( - x)^{4} + 4( - x)^{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 2x^{6} + 3x^{4} + 4x^{2} = f(x)\ \therefore f( - x) = f(x)$
$\Rightarrow f(x)$ is an even function.
$\Rightarrow f^{'}(x)$ is an odd function.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.