A convex function is a type of mathematical function where a line segment connecting any two points on the graph of the function lies above or on the graph itself. This property means that the function curves upwards, making it easier to find minimum values. In simpler terms, if you pick any two points on the curve, the straight line between them will never dip below the curve. Convex functions are important in various fields, including economics, optimization, and machine learning. They often have unique minimum points, which simplifies the process of finding optimal solutions. Common examples of convex functions include quadratic functions and exponential functions.