Definition:Critical Point
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Definition
Let $f: X \to Y$ be a smooth map of manifolds.
A point $x \in X$ is called a critical point of $f$ iff $d f_x: T_x \left({X}\right) \to T_y \left({Y}\right)$ is not surjective at $x$.
What does $d f_x$ mean in this context?
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