Concept

# Convex function

Summary
In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above the graph between the two points. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. A twice-differentiable function of a single variable is convex if and only if its second derivative is nonnegative on its entire domain. Well-known examples of convex functions of a single variable include a linear function f(x) = cx (where c is a real number), a quadratic function cx^2 (c as a nonnegative real number) and a exponential function ce^x (c as a nonnegative real number). In simple terms, a convex function refers to a function whose graph is shaped like a cup \cup (or a straight line like a linear function), while a concave function's graph is shaped like a cap \cap
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