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I assume Rolle came later since it is a specific instance of Mean Value

but Rolle's theorem is used to generalize into/prove Mean Value Theorem.

So did Rolle's theorem come first AND was used to prove Mean Value?

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user29418
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    I assume Rolle came first since it is a specific instance of Mean Value. Why would the more general one come first? And if it did, why would someone even bother to name the more specific one? – Bobbie D Mar 07 '17 at 02:55
  • The specific one is very useful? – user29418 Mar 07 '17 at 03:05
  • Still beautiful that a special case of the mean value theorem can be used to prove the mean value theorem. – Shashi Mar 07 '17 at 06:40
  • @BobbieD Brooke Taylor derived his series in 1715, Colin Maclaurin used the series around the origin in the mid 18th century. Therefore the Taylor Series came before the Maclaurin Series – user29418 Dec 24 '23 at 02:17

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Yes and No: Rolle's theorem did come first, but it was NOT used to prove the mean value theorem (MVT) when the MVT was first proved. The insight that the MVT is reducible to Rolle's theorem seems to have come later.

At the end of the 19th century the MVT was still research-level material. The burning issue of the day was whether the theorem requires the function to be differentiable or continuously differentiable. A controversy opposed Peano and Gilbert as to the validity of a proof given by Camille Jordan. A nice historical summary can be found in a pdf by Besenyei.

Mikhail Katz
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