Find the 5th degree Taylor poly and a bound for its error.

I have attached a doc with what I have so far. I don't understand how to bound the error when it depends on some c we don't know anything about.

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- Oct 12th 2011, 06:11 PMveronicak5678Taylor Remainder Theorem
Find the 5th degree Taylor poly and a bound for its error.

I have attached a doc with what I have so far. I don't understand how to bound the error when it depends on some c we don't know anything about. - Oct 12th 2011, 09:33 PMchisigmaRe: Taylor Remainder Theorem
- Oct 13th 2011, 12:07 PMveronicak5678Re: Taylor Remainder Theorem
Why is c between 0 and 1? I forgot to mention that -10 <= x <= 10.

I'm confused about finding the max values when I have two variables in the remainder term. How do I find the max value when I need to know the values of c and x? - Oct 13th 2011, 10:13 PMchisigmaRe: Taylor Remainder Theorem
- Oct 14th 2011, 07:42 AMveronicak5678Re: Taylor Remainder Theorem
I have found that for c between -10 and 10 f has a max at c= 1.27144933065785

but what about the x^6? Do I need to worry about that? - Oct 14th 2011, 11:55 AMchisigmaRe: Taylor Remainder Theorem
- Oct 14th 2011, 12:54 PMveronicak5678Re: Taylor Remainder Theorem
I don't understand where you got that number. Am I correct that to get the error, we first find the max error for the part of the function involving c for c between -10 and 10, ans then you find the max error for the function involving x for x between -10 and 10 and multiply? Doing that, we get 1.2714e+006. What am I doing wrong?

- Oct 15th 2011, 12:04 AMchisigmaRe: Taylor Remainder Theorem
I apologize with Veronika for the fact that in hand computation I'm very poor [(Doh) ...], so that I decided to use my computer to solve her problem...

The first step is to find the extreme points of the function...

(1)

According to my computer the derivative of (1) vanishes for and and because is and it must be [tex] . Now is so that for is...

(2)

Kind regards

- Oct 15th 2011, 11:19 AMveronicak5678Re: Taylor Remainder Theorem
Does this seem right? It looks like such a large value.