ISI PEA 2010 Q 25

[eco'17]

http://economicsentrance.weebly.com/uploads/1/1/0/5/1105777/msqe2010.pdf

Its given that f(1)=0 and f'(x)>f(x) for all x>1
so what i did f'(x)>0 therefore increasing function hence f(x)>0

but my question is can I do this question this way because its given f'(x)>f(x) for x>1 and not equal to 1
please help!

[Halflife]

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[Halflife]

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[eco'17]

thanks!