Question

If h(x) = f(x) + f(–x) then h(x) has got an extreme value

where f '(x) is -

• A. An even function
• B. An odd function
• C. Zero
• D. None of these

Answer 1

Answer: (A)

An even function

Answer 2

h(x) = f(x) + f(–x) ⇒ h' (x) = f '(x) – f '(– x)

⇒ If h(x) has extreme point ⇒ h'(x) = 0

⇒ f '(x) = f '(–x)

⇒ f '(x)is even function.