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This lecture covers applications of differential calculus, including theorems related to continuity and differentiability, such as Rolle's theorem and the rule of Bernoulli-L'Hospital. It also discusses the study of functions, convexity, concavity, local and global extrema, inflection points, and the graph of functions. The lecture provides examples and criteria for determining convexity and concavity, as well as identifying stationary points and inflection points.