The concavity of the graph of a function refers to the curvature of the graph over an interval; this curvature is described as being concave up or concave down. Generally, a concave up curve …

In mathematics, a concave function is one for which the function value at any convex combination of elements in the domain is greater than or equal to that convex combination of those domain …

Concavity describes the shape of the curve. If the average rates are increasing on an interval then the function is concave up and if the average rates are decreasing on an interval then the …

Dec 21, 2020 · We have identified the concepts of concavity and points of inflection. It is now time to practice using these concepts; given a function, we should be able to find its points of …

Sal introduces the concept of concavity, what it means for a graph to be "concave up" or "concave down," and how this relates to the second derivative of a function.

For concavity, we want to zoom out a bit, so the graph curves up or down from a line. We say that a graph is concave up if the line between two points is above the graph, or alternatively if the …

Jul 23, 2025 · Concavity in a curve refers to its curvature, or the way it bends. If a curve is concave up, it opens upward like a cup, while if it's concave down, it opens downward like a …

Note that we need to compute and analyze the second derivative to understand concavity, so we may as well try to use the second derivative test for maxima and minima.

A function’s concavity describes how its graph bends—whether it curves upwards like a bowl or downwards like an arch. Previously, concavity was defined using secant lines, which compare …

Being able to determine the above-described concavity (up or down) of a function on various intervals and to locate a function's points of inflection will help us in a substantial way in …