f(x+y 2 ) = f(x) + [f(y)] 2 f is not 0 f is diff. at 0 then find f ' (0)

f(x+y2) = f(x) + [f(y)]2

f is not 0 f is diff. at 0 then find f ' (0)  


1 Answers

Badiuddin askIITians.ismu Expert
148 Points
13 years ago

Dear dinesh

f(x+y2) = f(x) + [f(y)]2

put y=x

f(x+x2) = f(x) + [f(x)]2


(1+2x)f'(x+x2) = f'(x) + 2f'(x)[f(x)]

put x=0

f'(0)=f'(0) + 2'f(0)[f(0)]

or   f'(0)[f(0)]=0

so f'(0) =0

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