If $h(x)=f(x)+f(-x)$, then $h(x)$ has go

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Applications of Derivatives

Question:

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

Options:

an even function

an odd function

zero

none of these

Correct Answer:

an even function

Explanation:

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.