Critical points are specific values in a mathematical function where the function's derivative is either zero or undefined. These points are important because they can indicate where the function changes direction, such as reaching a maximum or minimum value. Identifying critical points helps in understanding the overall behavior of the function. In the context of calculus, critical points are often used in optimization problems to find the best possible solutions. For example, when analyzing the function of a profit or cost, determining the critical points can reveal the most efficient production levels or pricing strategies.