- #1

- 84

- 0

if we have a function that has n derivatives on the interval [a,b] and n+1 derivatives on (a,b). fix a point Xo [tex]\in[/tex] (a,b). then for any x [tex]\in[/tex] (a,b) there exists a number Z between Xo and x ....put z into the lagrange formula and it gives you the bounds on the error from what i understand?

The issue im having is how to we pick the interval (a,b) ....

for example in the text the most basic question is e

^{x}

if i wanted to estimate the value of e with a 3rd degree taylor polynomial then I calculate the 4 derivatives of e

^{x}(which are all the same) put the first 3 derivatives in a taylor series.. and then for the remainder term use the fourth derivative and then ?

let Xo = 1 .... then the interval (a,b) needs to contain 1. so for example can i pick the interval (1/2, 6) or is it better to have a smaller interval?