A convex function is a type of mathematical function defined on an interval or a convex set. It has the property that a line segment connecting any two points on the graph of the function lies above or on the graph itself. This means that for any two points, the function's value at any point on the line segment between them is less than or equal to the values at the endpoints. Convex functions are important in various fields, including economics, optimization, and machine learning. They often have a single minimum point, making them easier to analyze and optimize. Examples of convex functions include quadratic functions and the exponential function.