Question

If $f(x)$ is an even function and $f^{\prime }(x)$ exists, then $f^{\prime }(e)+f^{\prime }(-e)$ is

• A. $\ge 0$
• B. 0
• C. > 0
• D. < 0

Answer 1

Answer: (B)

Since, $f(x)$ is an even function, therefore $f^{\prime }(x)$ is an odd function.
ie, $f^{\prime }(-e)=-f^{\prime }(e)$
$\therefore f^{\prime }(e)+f^{\prime }(-e)=0$