Extrema and Implicit Functions

This lecture covers the sufficient condition for a function to have a local extremum in the cases of two and three variables, with examples. It also discusses extrema of a continuous function on a compact subset, along with implicit functions. The slides detail the conditions for local extrema in two and three variables, as well as the theorem for a continuous function on a compact set. Additionally, the concept of implicit functions is explored, including examples and theorems. The lecture concludes with practical applications, such as finding the absolute minima and maxima of functions on specific domains.