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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 \( g : [a, b] \to \mathbb{R} \) be a function such that:

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

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