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.

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.

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