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I found \(f(0)=0\) but now I am not seeing how to proceed. Just a hint would be nice.

I further think I proved that the function is odd, though I think that doesn't really help me :/

use the definition of a derivative

the fact that it is odd does seem to help with the last part

\[f'(0)=\lim_{x\to0}\frac{f(x)-f(0)}{x-0}\]

limit f(x)-f(0) something...

okay so that is f'(0)=1, on to the last part
you say the oddness could help?

yes

can I use the derivative of an odd function is even?

don't need it

use the definition of a derivative again

that's what I'm doing, let me toy for a sec...

I found f(x) ;)

...if you would be so kind

if you know f'(x) and that f(0)=0 then finding f(x) is really easy :)

\[f'(x)=\lim_{y\to x}\frac{f(y)-f(x)}{y-x}\]

\[f(y)-f(x)=f(y)+f(-x)\]

does that help?

ok

yes

gotta go...fun problem...I'll post it later if you like

always a pleasure :)