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Let f (x) be a continuous and differenti...

Let `f (x)` be a continuous and differentiable function satisfying `f (x+y) = f(x) f (y) AA x, y in R` if `f (x)` can be expressed as `f (x) =1 +x P (x)+ x ^(2)Q(x)` where `lim _(xto0) lim P(x)=a and lim _(xto0) lim Q (x) =b,` then f '(x) is equal to :

A

`af (x)`

B

`bf (x)`

C

`(a+b) f (x)`

D

`(a+2b) f(x)`

Text Solution

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The correct Answer is:
A
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