- #1

- 2

- 0

"If a function f is differentiable through order n+1 in an interval I containing c, then, for each x in I, there exists z between x and c such that

f(x) = f(c) + f'(c)(x-c) + ... + R

_{n}(x)

where

R

_{n}(x) = (f

^{n+1}z)/(n+1)! (x-c)

^{n+1}."

Forgive me for not knowing the coding and such. So, the equation(s) might look a bit sloppy.

The book goes on to say:

"One useful consequence of this theorem is that |R

_{n}x| [tex]\leq[/tex] |x-c|

^{n+1}/(n+1)! max |f

^{n+1}z|"

This part does not make sense to me. Again, sorry for making the formulas appear sloppy. I do not quite understand what that last inequality means. And, in addition, I do not know what max |f

^{n+1}z| refers to. Thanks for any help, and for even reading this.