Derivative and Local Extrema Study

This lecture covers the study of local extrema using derivatives, focusing on points where the function is differentiable and its derivative is zero. It explains the conditions for identifying local maxima and minima, emphasizing the importance of continuity at these points. The lecture also discusses examples to illustrate the concepts and provides a detailed proof of the criteria for determining local extrema. Additionally, it explores the significance of the sign change of the derivative at critical points and the implications for identifying extremums.