Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. In simple terms, a convex function graph is shaped like a cup (or a …

Jul 3, 2025 · A convex function curves upwards, meaning that a straight line between any two points on the graph will lie above or on the graph. A concave function curves downwards, …

Convex functions are real valued functions which visually can be understood as functions which satisfy the fact that the line segment joining any two points on the graph of the function lie …

Dec 21, 2020 · We have been learning how the first and second derivatives of a function relate information about the graph of that function. We have found intervals of increasing and …

In convex analysis, a closed function is a convex function with an epigraph that is a closed set. The epigraph is the set of points laying on or above the function’s graph.

Convex and Concave Curves revision and practice questions. MME gives you access to maths practice questions, worksheets and videos.

In the sections below, I’ll explain how to determine whether a function is concave or convex, either by examining its graph or by analyzing its derivative.

Figure 1: An illustration of the de nition of a convex function In words, this means that if we take any two points x; y, then f evaluated at any convex combination of these two points should be …

Prove that \ (cf\), \ (f + g\), and \ (\max \ {f, g\}\) are convex functions on \ (I\), where \ (c \geq 0\) is a constant. Find two convex functions \ (f\) and \ (g\) on an interval \ (I\) such that \ (f \cdot g\) …

Although they are both increasing, the first graph’s rate of increase is itself increasing whereas the rate of increase is decreasing in case of the second graph.