A sufficiently differentiable function can be approximated near a point by a polynomial built from its derivatives at that point, the Taylor polynomial, with a remainder term that can be bounded explicitly. Named for Brook Taylor, it is the basis for power series expansions throughout analysis.
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StatementTaylor's theorem states that a k-times differentiable function can be approximated near a given point by a polynomial of degree k, called the k-th order Taylor polynomial, built from the function's own derivatives at that point. 1 Classification
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Source Brook Taylor, Biography (MacTutor History of Mathematics)
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1. Taylor's Theorem (Wikipedia)
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Taylor's theorem is named after Brook Taylor, who stated a version of it in 1715, although an earlier version of the result was already mentioned in 1671 by James Gregory.
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Taylor's theorem is named after Brook Taylor, who stated a version of it in 1715, although an earlier version of the result was already mentioned in 1671 by James Gregory.
Proved By: Brook Taylor, Lead
Taylor's theorem is named after Brook Taylor, who stated a version of it in 1715, although an earlier version of the result was already mentioned in 1671 by James Gregory.
View the Source Brook Taylor, Biography (MacTutor History of Mathematics)
Principal Result Of: Brook Taylor, Biography textQuote, Principal Result Of: Brook Taylor, Biography text
In fact the first mention by Taylor of a version of what is today called Taylor's Theorem appears in a letter which he wrote to Machin on 26 July 1712 .
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