Concave means "hollowed out or rounded inward" and is easily remembered because these surfaces "cave" in. The opposite is convex meaning "curved or rounded outward." Both words have been around for centuries but are often mixed up. Advice in mirror may be closer than it appears. Convex Concave and convex are literal opposites—one involves shapes that curve inward and the other involves shapes that curve outward. The terms can be used generally, but they're often used in technical, scientific, and geometric contexts.
Concave vs. Convex The Correct Way to Use Each Confusing Words
$\begingroup$ If you know the standard English meaning of the words convex and concave, you can remember that for a convex function it is the epigraph that is convex, and for a concave function it is the epigraph that is concave. Failing that, the "cave" mnemonic mentioned by @SeanRoberson seems unforgettable. $\endgroup$ 2 Answers Sorted by: 6 A function with this graph is quasiconcave, but not concave. It can be proved that a function f is quasiconcave if and only there exists x0 s.t. f is nondecreasing for x
x0. I don't write precisely about a domain. It should be interval on a real line. Definition: An object or function is convex if it curves outward, or in other words, bulges out. Everyday Examples: An eye A speed bump. A magnifying glass. A globe. A triangle. Ways to Remember Concave: Think "Con-cave"; it has a "cave" or an inward dip. Convex: Think of "Con-vex" as "convicts" trying to escape, bulging outwards. Company Concave vs. Convex Marko Ticak Updated on May 22, 2019 Grammar Concave describes shapes that curve inward, like an hourglass. Convex describes shapes that curve outward, like a football (or a rugby ball). If you stand in front of a concave mirror, your reflection will look taller.
Quelle différence entre concave et convexe ? La culture générale
De nition 1. A function f : n R ! R is convex if its domain is a convex set and for all x; y in its domain, and all 2 [0; 1], we have f( x + (1 )y) f(x) + (1 )f(y): Conversely, if the second derivative is positive at any point, we say that the curve is convex at that point. It follows that there is an interval around a maximum that is concave and an interval around a minimum that is convex. See Example 1. The point where a curve changes from being concave to convex or vice versa is known as an inflection. In mathematics, a concave function is one for which the value at any convex combination of elements in the domain is greater than or equal to the convex combination of the values at the endpoints. Equivalently, a concave function is any function for which the hypograph is convex. Convex is also used as a noun in in mathematics and geometry, i.e. it is a name for a type of shape or outwardly curved line. Concave vs. Convex Examples Here are some examples of concave and convex used in a sentence: The table was not flat, but sloped outwards, slightly convex like the glass of a watch. The corset made her waist look tiny. 
Difference between Concave and Convex Lens
In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset contains the whole line segment that joins them. Equivalently, a convex set or a convex region is a subset that intersects every line into a single line segment (possibly empty). Concave and convex are both adjectives that describe the shape and curvature of objects, i.e., nouns.. For example, the inside of a bowl or a spoon have surfaces that are concave, and curve inwards. Therefore, these objects can be described as 'concave' in shape.. Concave shapes are thinner in the middle than they are at the edges; whereas convex shapes have a thicker middle and are.
Concave is an adjective that describes a surface that curves inward, or is thinner in the middle than on the edges. In ordinary usage, concave and convex are typically used when referring to glass surfaces, like the lenses of optical viewing equipment. The side mirror of a car has a concave surface. The inside surface of most eyeglasses is concave. First, the strongly convex-strongly concave setting is fundamental. Via reduction [24], an efficient algorithm for this setting implies efficient algorithms for other settings, including strongly convex-concave, convex-concave, and non-convex-concave settings. Second, Zhang et al. [42] recently proved a gradient complexity lower bound 1 q L x. 
mnemonic How to remember which function is concave and which one is convex? Mathematics
(b) f is strictly convex i for any a;b2C and any 2(0;1), the above inequality is strict. The following equivalence is immediate from the de nitions. Theorem 1. Let C RN be non-empty and convex and let f: C!R. fis convex i fis concave. fis strictly convex i fis strictly concave. f is both concave and convex i for any a;b2RN and any 2(0;1), f( a+ This short clips explains the difference between convex and concave preferences-- without math.
