\(
\newcommand{\cat}[1] {\mathrm{#1}}
\newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})}
\newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}}
\newcommand{\multiBetaReduction}[0] {\twoheadrightarrow_{\beta}}
\newcommand{\betaReduction}[0] {\rightarrow_{\beta}}
\newcommand{\betaEq}[0] {=_{\beta}}
\newcommand{\string}[1] {\texttt{"}\mathtt{#1}\texttt{"}}
\newcommand{\symbolq}[1] {\texttt{`}\mathtt{#1}\texttt{'}}
\)
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.
Source
p260
