The polar of the cone of linearized directions

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Explores directional derivatives in two-variable functions and extremum points.

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Explores the Local Inversion Theorem and extremum points in functions.

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Discusses optimization techniques, focusing on local and global extrema in functions.

Covers the optimization of functions, focusing on finding the maximum and minimum values over a given domain.

Explores optimization on convex sets, including KKT points and tangent cones.

Covers the theorems on continuous functions and extremums in compact sets.

Covers derivatives, reciprocal functions, Rolle's theorem, and extremum local concepts.

Covers the discussion of local extrema, concavity, convexity, and inflection points in functions.