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  4. If f (x ) is an even function and f'(x) exists, then f'(e ) + f'(-e ) is

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Q. If $f (x )$ is an even function and $f'(x)$ exists, then $f'(e ) + f'(-e )$ is

KCETKCET 2008Continuity and Differentiability

Solution:

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