Extrema, or extremes, refer to the highest and lowest values of a function or dataset. In mathematics, these points are crucial for understanding the behavior of functions, especially in calculus. The highest point is called the maximum, while the lowest point is known as the minimum. Identifying these points helps in optimization problems, where one seeks to maximize or minimize a particular quantity. In real-world applications, extrema can be found in various fields such as economics, physics, and engineering. For example, in economics, businesses may analyze profit functions to determine the maximum profit point. Similarly, in physics, understanding the extremes of a trajectory can help in predicting the motion of objects.