\(
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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:
- \( g \) is [something and something].
- [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.
