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

If `f(x-y), f(x) f(y) and f(x+y)` are in A.P. for all `x , y ,and f(0)!=0,` then (a) `f(4)=f(-4)` (b) `f(2)+f(-2)=0` (c) `f^(prime)(4)+f^(prime)(-4)=0` (d) `f^(prime)(2)=f^(prime)(-2)`

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