Concave function - Wikipedia
网页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 …
Convex and Concave Curves | Revision | MME - MME Revise
网页We define a curve f (x) as convex or concave when we observe the behaviour of f'' (x). Make sure you are happy with the following topics before continuing. Stationary Points. A Level AQA Edexcel OCR. Distinguishing Between Convex and Concave. Convex curves curve downwards and concave curves curve upwards.
Concave Upward and Downward - Math is Fun
网页When the slope continually increases, the function is concave upward. When the slope continually decreases, the function is concave downward. Taking the second derivative actually tells us if the slope continually increases or decreases. When the second derivative is positive, the function is concave upward.
Difference between Convex and Concave Curves
网页In a concave curve, a straight line connecting any two points on the curve lies entirely under the curve. However, in a convex curve, a straight line joining any two points lies totally above the curve. Both the curves are regarded opposite to each other.
Concave vs Convex - Science Notes and Projects
网页2023年9月9日 · Concave lenses focus light inside the curve of the lens, while convex lenses focus light using the outer curve. A lens that curves like a “C” (no flat side) is both concave or convex, depending on which side of the lens you view from.
Concavity - Math.net
网页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 has a shape resembling "∪" and a concave down curve has a shape resembling "∩" as shown in the figure below. Concave up.
Why does "convex function" mean "concave *up*"?
网页A function f: R → R is convex (or "concave up") provided that for all x, y ∈ R and t ∈ [0, 1], f(tx + (1 − t)y) ≤ tf(x) + (1 − t)f(y). Equivalently, a line segment between two points on the graph lies above the graph, the region above the graph is convex, etc. I want to know why the word "convex" goes with the inequality in this ...
Introduction to Concave and Convex Functions - YouTube
网页An introduction to what makes a curve concave and convex and a simple example of when parts of a curve can be concave and the other parts convex. https://ALe...
Concave Definition (Illustrated Mathematics Dictionary) - Math is …
网页Illustrated definition of Concave: Curved inwards. Example: A polygon (which has straight sides) is concave when there are dents or indentations...
Concave in Geometry | Definition, Shapes & Functions
网页2023年11月21日 · If a shape or polygon is concave, there is some place on it where a line drawn between two points in the shape will go outside the shape. For a mathematical definition, a concave shape will...