A function f is concave over a convex set if and only if the function −f is a convex function over the set. The sum of two concave functions is itself concave and so is the pointwise minimum of two concave …

Example 2: Concavity from a Table of Values The value, V, of a car after t years is given in the table below. Is the value increasing or decreasing? Is the function concave up or concave down?

Jul 3, 2025 · In mathematics, convex and concave functions describe how curves behave in terms of their curvature. A convex function curves upwards, meaning that a straight line between any two …

Sep 9, 2023 · Learn the difference between concave vs convex for lenses, mirrors, polygons, and mathematical functions. See how to remember the difference.

A function can be both concave up and down because the function's concavity switches at one or more points. A point at which a function's concavity changes is called an inflection point.

If, for example, the mountain is a perfect dome (half of a sphere), then this condition is satisfied, so that the function defined by its surface is concave. The condition is satisfied also if the mountain is a …

This is just a quick and condensed note on the basic definitions and characterizations of concave, convex, quasiconcave and (to some extent) quasiconvex functions, with some examples.

Fig.6.2 - Pictorial representation of a convex function and a concave function. We can state the definition for convex and concave functions in the following way:

Example Suppose that a strictly positive random variable has expected value and it is not constant with probability one. What can we say about the expected value of , by using Jensen's inequality? The …

In convex analysis, a non-negative function f : Rn → R+ is logarithmically concave if its domain is a convex set, and if it satisfies the inequality