Supporting Hyperplanes

This lecture delves into the concept of supporting hyperplanes for differentiable functions in higher dimensions, aiming to approximate the function graph by hyperplanes. Starting with the tangent line in one dimension, the instructor explains the transition to hyperplanes in higher dimensions, emphasizing the normal vector and the equation of hyperplanes. Linear approximations and supporting hyperplanes are explored, showcasing the process in both one and multiple dimensions. Through detailed examples, the audience learns how to determine the supporting hyperplane and the normal vector, as well as calculate the linear approximation for a given function at a specific point.