critical point

by cjeris

Sat Nov 13 1999 at 9:18:32

A critical point of a mapping between one manifold and another is a point where the derivative has less than the maximum possible rank. In one variable this means a zero of the derivative. In general this is a point near which the mapping squashes one or more dimensions of the domain space to nothing, although it is risky to assume too much from this intuitive picture.

by fscker

Fri Nov 09 2001 at 22:15:23

If there is a function f on an interval I which contains the point c, c is a critical point if at least one of the following is true:

1. c is an end point on the interval I.
2. c is a stationary point(Where the slope of the tangent(derivative) is equal to 0).
3. c is a singular point(Where the derivative does not exist).

Critical points can help you find out where the function is increasing and/or decreasing which in turn can help you find minima and maxima.

point of inflection	minima and maxima	supercritical fluid	Lyapunov stability
The Varsity Boat Race 2003	Compaq keyboards with a delete bar where the space bar is	Landau Theory	Derivative
The Critical Exponent	March 23, 2006	Unicode Middle Eastern Scripts	critical percolation
honeymoon salad	TiHKAL	HTML heading tags	Demonyms of Australia
P Cygni	Gulf of Mexico dead zone	Mean value theorem	logistic map
Gak	Delta epsilon proof	Uncle	Rationalism