Which theorem came first: Rolle or Mean Value?

Question

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?

Answer 1

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.