Convex curve - Wikipedia
In geometry, a convex curve is a plane curve that has a supporting line through each of its points. There are many other equivalent definitions of these curves, going back to Archimedes. …
Convex and Concave Curves | Revision | MME - MME Revise
An easy way to test for both is to connect two points on the curve with a straight line. If the line is above the curve, the graph is convex . If the line is below the curve, the graph is concave .
Convex function - Wikipedia
In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above or on the graph between the two points. …
Convex and Concave Functions - GeeksforGeeks
2024年9月22日 · In mathematics, convex and concave functions are functions with different curvature of graphs. A convex function curves upwards, meaning that any line segment …
Geometrically, the line segment connecting (x;f(x)) to (y;f(y)) must sit above the graph of f. If f is continuous, then to ensure convexity it is enough to check the de nition with
Convex Function: Definition, Example - Statistics How To
Graphical Examples of Convex and Non Convex Functions. The easiest way to figure out if a graph is convex or not is by attempting to draw lines connecting random intervals. On the left …
Geometrically, convexity means that the line segment between two points on the graph of f lies on or above the graph itself. See Figure 2 for a visual. Strict convexity means that the line …
3.1 Concave and convex functions of a single variable
A function of a single variable is concave if every line segment joining two points on its graph does not lie above the graph at any point. Symmetrically, a function of a single variable is convex if …
Example: the function f(x) = 1=x is convex on (0;1) and concave on (1 ;0). Geometric meaning: f is weakly convex i for each a;b 2I the interval from (a;f(a)) to (b;f(b)) is weakly above the graph of …
condition has a clear geometric meaning. Namely, the line segment connecting (x; f(x)) and (y; f(y)) always lies above the graph of f. called concave if its negative is convex. Apparently every …