# Intuition behind Taylor's Theorem [closed]

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?

## closed as off-topic by Andrés E. Caicedo, user10354138, John B, max_zorn, GibbsNov 9 '18 at 22:06

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• Can you understand intuitively how to answer your questions when $n=0$? – Ethan Bolker Nov 2 '18 at 19:48