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Math and science::Analysis::Tao::10: Differentiation of functions

Rolle's theorem

Rolle's theorem

Let a<b be real numbers, and let g:[a,b]→R be a function such that:

  1. g is [something and something].
  2. [an equality].
Then there exists an x∈(a,b) such that g′(x)=0.

A corollary of Rolle's theorem is the [something] theorem.