Originally Posted by

**pirateboy** I just want to make sure I'm doing this right.

So we're given the funciton

$\displaystyle f(x) = x \ln(x)$

we're first asked to find the 4th degree taylor polynomial centered at $\displaystyle a=1$

we're then asked to use taylor's inequality to bound the error in the approximation

$\displaystyle f(x)\approx T_4(x) \text{ for } x\in\left[0.2,1.8\right]$

we recall

$\displaystyle \left|R_n(x)\right|\leq \frac{M}{(n+1)!}\left|x-a\right|^{n+1}$

well, $\displaystyle f^{(5)}(x) = \frac{-6}{x^4}$ so i'd want to use $\displaystyle x=.2$?

if i understand correctly, I want M to be as big as possible. and since this is centered at a=1, this would give me

$\displaystyle \displaystyle \left|R_4(x)\right|\leq \frac{f^{(5)}(.2)}{5!}\left|.2-1\right|^{5} = \frac{\frac{-6}{(.2)^4}}{5!}(.8)^5 = -10.24$

this just seems like quite a big maximum error to me.

if someone could confirm that this is the error i should be getting, that'd be great.