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If f(x-y),f(x)*f(y),f(x+y) are in A.P f...

If `f(x-y),f(x)*f(y),f(x+y)` are in A.P for all `x,y in R " and " f(0) ne 0`, then
(a) `f'(x)` is an even function
`(b)f'(1)+f'(-1)=0`
`(c)f'(2)-f'(-2)=0`
`(d)f'(2)-f'(-2)=0`

A

f'(x) is an even function

B

f'(1)+f'(-1)=0

C

f'(2)-f'(-2)=0

D

f'(3)+f'(-3)=0

Text Solution

Verified by Experts

The correct Answer is:
B, D
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