This is a question about proving the Newton Raphson formula (I think!), and I'm not quite sure what it is asking for. I would rather I wasn't told the answer as I would like to figure it out myself, unless of course it is difficult to explain what the question means without answering it!
"Write down the Taylor series for a function f evaluated at x+h in terms of f(x) and its derivatives evaluated at x"
Specifically,
1.Does this mean the expansion of f(x) about x=-h (so that terms are (x+h)?
2.Or perhaps the expansion of f(x+h) about x? At the moment, I think it seems most likely that they are asking for this, however I would then think that the derivatives would be evaluated at (-x), as they are evaluated at (a) for an expansion of f(x-a)...