If $h(x)=f(x)+f(-x)$, then $h(x)$ has got an extreme value at a point where f'(x) is
Answer & explanation
Correct answer: option 1
We have,
$h(x)=f(x)+f(-x)$
$\Rightarrow h'(x)=f'(x)-f'(-x)$
If h(x) has got an extreme value at a point, then
$h'(x)=0$
$\Rightarrow f'(x)=f'(-x)$
$\Rightarrow f'(x)$ is an even function.