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 the weighted average of those points is less than or equal to the weighted average of the function's values at those points. Convex functions are important in various fields, including optimization and economics. They often have unique minima, making them easier to analyze and solve. Common examples include quadratic functions and exponential functions, which exhibit this convexity property.