# How do you find the smallest value of #n# for which the Taylor Polynomial #p_n(x,c)# to approximate a function #y=f(x)# to within a given error on a given interval #(c-r,c+r)#?

##### 1 Answer

Sep 20, 2014

Let

The error can be estimated by

where

since

if we know that the absolute value of all derivatives of $f(x)$ are bounded by some fix value

Find