I have a question on Newton Raphson's method. The method is briefly as follows
Original resource is from https://sites.stat.washington.edu/adobra/classes/536/Files/week1/newtonfull.pdf
My question is why the second order Taylor expression is used instead of first order or higher order Taylor expression? Can you please share your ideas with me? thank you.
Not seeking the root for the function itself, but for its critical value.
To find min/max we set the derivative to zero i.e, raise differentiation to next order by one more time differentiation.
So we have to subtract for each successive iterate at time of drawing tangent of graph
$$ \dfrac {f'}{f''}\text{ instead of }\dfrac {f}{f'}. $$