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If f(x+y)=2f(x) f(y) for all x,y where f...

If `f(x+y)=2f(x) f(y)` for all x,y where f'(0)=3 and f(4)=2, then f'(4) is equal to

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The correct Answer is:
4
`f(4)=limg_(hrarr0)(f(4+h)-f(4))/h`
`=limg_(hrarr)(f(4+h)-f(4+0))/h`
`= lim_(hrarr0)(2f(4)f(4)-2f(4)f(0))/h` (using `f(x+y)=2f(x)f(y))`
`=2f(4).lim_(hrarr0)(f(h)-f(0))/h=2f(4)f(0)=2xx3xx4=4`
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