\begin{definition}[Definition:Critical Point/Smooth Manifold]
Let $M$ be a smooth manifold.
Let $f \in \map {\CC^\infty} M : M \to \R$ be a smooth real-valued function.
Let $p \in M$ be a base point in $M$.
Let $\rd f_p$ be the differential of $f$ at $p$.
Suppose $\rd f_p = 0$.
Then $p$ is called a '''critical point of $f$'''.
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\end{definition}