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Corollaries from Taylor's theorem

All corollaries from Taylor's theorem.

[COROLLARY]

For some $c$ between $a$ and $x$ ,

\frac{f(x)-f(a)}{x-a}=f'(c)

whenever $x\ne a$ and the hypotheses of the Mean Value Theorem hold.

This page builds on Taylor polynomials.

Part of the thread Local approximation, in 7 places.

Replace a hard object by a simple model that matches it near a point, and bound the error.