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Extrema

In hx = fx + ...

Question

In h(x) = f(x) + f(-x), then h (x) has got an extreme value at a point where f'(x) is

even function.

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odd function.

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zero

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None of these

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Solution

The correct option is A
even function.

We have, h'(x) = f'(x) - f'(-x)
For extreme value of h(x), h'(x) = 0
$\Rightarrow$ f'(x) = f'(-x) $\Rightarrow$ f'(x) is an even function.

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