critical point theory

Critical point theory studies the behavior of functions by examining points where their derivatives are zero or undefined, known as critical points. These points help identify features such as peaks, valleys, and saddle points on graphs, which are essential for understanding the function’s overall shape. In applications like optimization, critical point theory aids in finding maximum or minimum values, guiding decision-making and problem-solving across various fields. Essentially, it provides tools to analyze how functions change and to locate important features that determine their behavior.