Critical value

Critical value may refer to:


In differential topology, a critical value of a differentiable function ƒ : MN between differentiable manifolds is the image (value of) ƒ(x) in N of a critical point x in M.[1]


In statistical hypothesis testing, the critical values of a statistical test are the boundaries of the acceptance region of the test.[2] The acceptance region is the set of values of the test statistic for which the null hypothesis is not rejected. Depending on the shape of the acceptance region, there can be one or more than one critical value.

Complex dynamics

In complex dynamics, a critical value is the image of a critical point.


  1. do Carmo, Manfredo Perdigão (1976). Differential Geometry of Curves and Surfaces. Prentice Hall. ISBN 0-13-212589-7.
  2. Hughes, Ann J.; Grawoig, Dennis E. (1971). Statistics: A Foundation for Analysis. Reading, Mass.: Addison-Wesley. p. 191. ISBN 0-201-03021-7.
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