Intuition behind Taylor's Theorem

Question

What is an intuitive explanation for the fact that the remainder of a Taylor polynomial has this equivalency? Why is z necessarily between x and c? Why does such a value for z exist in the first place?

Can you understand intuitively how to answer your questions when $n=0$? — Ethan Bolker, Nov 02 '18 at 19:48

William Elliot · Accepted Answer · 2018-11-03T10:45:23.010

1

For n = 0, it's applying the mean value theorem to f(x).
For n = 1, it's applying the mean value theorem to
f(c) + f'(c)(x - c).
And so to n. So it's basically an elaborate MVT.

edited Nov 03 '18 at 10:45

answered Nov 03 '18 at 05:25

William Elliot

17,598

1

Please go into further detail – MacroGuy Nov 03 '18 at 05:25

Intuition behind Taylor's Theorem

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