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Prove Taylor's Inequality for $ n = 2, $ that is, prove that if $ \mid f''' (x) \mid \le M \text { for }

\mid x - a \mid \le d, $ then

$ \mid R_2 (x) \mid \le \frac {M}{6} \mid x - a \mid^3 $ for $ \mid x - a \mid \le d $

$\left|R_{2}\left(x_{2}\right)\right| \leq \frac{1}{6} M|x-a|^{3}$

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Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

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