\begin{definition}[Definition:Conjugate Point (Calculus of Variations)/Definition 2]
Let $y = \map y x$ and $y^* = \map {y^*} x$ be extremal functions.
Let:
:$M = \tuple {a, \map y a}$
:$\tilde M = \tuple {\tilde a, \map y {\tilde a} }$
Let $y$ and $y^*$ both pass through the point $M$.
Let:
:$\map {y^*} {x - \tilde a} - \map y {x - \tilde a} = \epsilon \size {\map {y^*} {x - \tilde a} - \map y {x - \tilde a} }_1$
where:
:$\size {\map {y^*} {x - \tilde a} - \map y {x - \tilde a} }_1 \to 0 \implies \epsilon \to 0$
Then $\tilde M$ is '''conjugate''' to $M$.
{{DefinitionWanted|norm in $C^1$ space}}
\end{definition}