Math and science::Analysis::Tao::10: Differentiation of functions
Mean value theorem
Let \( a < b \) be real numbers, and let \( g : [a, b] \to \mathbb{R} \) be a
function continuous on \( [a, b] \) differentiable on \( (a, b) \). Then, there
exists an \( x \in (a, b) \) such that:
\[ g'(x) = \frac{g(b) - g(a)}{b - a} \]
The mean value theorem is a corollary of Rolle's theorem.
