Tangent planes and normal lines (basics and problems), Lecture notes of Applied Mathematics

Description:Tangent planesand normal linesare fundamental concepts in calculus and differential geometry that help us understand the behavior of curves and surfaces.In the context of curves, a tangent line represents a line that touches the curve at a specific point, sharing the same slope as the curve at that point. It provides information about the instantaneous rate of change or the direction of motion at that point. Tangent lines play a crucial role in finding derivatives, determining critical points, and understanding the local behavior of curves.On the other hand, normal planes are relevant in the study of surfaces. A normal plane is a plane that is perpendicular to the tangent line at a given point on the surface. It serves as a reference plane, helping us understand the orientation and behavior of the surface at that point. Normal planes are important in various applications, such as determining surface normals.