Derivative and Local Extrema Study

This lecture covers the study of local minima and maxima of a function through its derivative. It explains the conditions for a point to be a local extremum, emphasizing the importance of the derivative's sign change at that point. The lecture also discusses cases where the function is not differentiable at a point and how to identify local extrema in such scenarios. Additionally, it explores the significance of continuity in determining local extrema. Various examples are provided to illustrate the concepts, including the role of tangents and horizontal/vertical asymptotes in identifying local extrema.