Critical Point Theory is a branch of mathematics that studies the behavior of functions at their critical points, where the derivative is zero or undefined. These points are essential for understanding the function's local maxima, minima, and saddle points. By analyzing these critical points, mathematicians can gain insights into the overall shape and behavior of the function. This theory is widely used in various fields, including calculus, differential equations, and optimization. It helps in solving real-world problems, such as finding the best solutions in economics or engineering, by identifying optimal conditions and constraints through the examination of critical points.