I'm having some trouble understanding Newton's Method in terms of its application, no literal problem, just conceptual qualms. If I have a function (with only one real root for this example) that is continuous everywhere and differentiable everywhere, if I choose some arbitrary x value to use Newton's Method with, will it always converge on the real root?

Question

anonymous · Answer

On a polynomial, yes, but this is not necessarily so on all cases. Try graphing the slopes and using a more geometric approach; with it, it becomes pretty clear.

mendicant_bias · Answer

Okay, thanks. Yeah, I would like to avoid graphs at all costs if I can and just deal witht he algebra, but it makes sense that it's necessary.

mendicant_bias · Answer

*with the

anonymous · Answer

Here, let's see if this helps, and sorry for the crappy drawing.

mendicant_bias · Answer

Thanks. And lol, no, you have good handwriting, the drawing was good for being improptu.

mendicant_bias · Answer

ALSO...are those Sony NC-200's?

anonymous · Answer

Nah, this is a Turtle Beach gaming headset

anonymous · Answer

Couldn't quite catch your comment? Was it removed or something?

mendicant_bias · Answer

Yeah, I was just going to recommend getting a Sony NC-500 if you are an audiophile and ever have money to blow; they have an internal battery with a nineteen hour battery life, and when they say nineteen hours, they're probably actually being a little modest. I got a pair last year and it still can stay on for a huge amount of time on one charge. I deleted it, thought it was just glazed over/not responded to and felt dumb.

anonymous · Answer

Ahh, gotcha... I'll keep it in mind, mate