For the error bound for taylor's theorem, for the n+1 derivative evaluated at some c which maximizes the derivative my textbook says c must be between a and x..but today my teacher said that c must be between absolute value x and negative absolute value x, which is different than I thought.(adsbygoogle = window.adsbygoogle || []).push({});

An example would be calculating the error of using a second degree taylor polynomial to estimate e^x at x=-1...the n+1 derivative would be e^x, so the question would be do I use 0 because 0 maximizes e^x on [-1,0] or do I use 1 because of absolute value x being 1 and 1 maximizes e^x on [-1,1].

Hopefully my question makes sense, just to reiterate I am wondering if c is between a and x (which is what textbook says and is what I thought in the past) or between absolute value x and negative absolute value x.

Additionally I already tried to talk to my teacher to clarify and he insisted it must be between absolute value x and negative absolute value x...but in the past I learned it was x and a which is confirmed by my book.

Any help on this is appreciated

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# Taylor's Theorem Error Bound

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