Critical value may refer to:
In differential topology, a critical value of a differentiable function ƒ : M → N between differentiable manifolds is the (value of) ƒ(x) in N of a critical point x in M.
In statistical hypothesis testing, the critical values of a statistical test are the boundaries of the acceptance region of the test. 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.
In complex dynamics, a critical value is the image of a critical point.
In medicine, a critical value or panic value is a value of a laboratory test that indicates a serious risk to the patient. Laboratory staff may be required to directly notify a physician or clinical staff of these values.
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In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus. Any manifold can be described by a collection of charts (atlas). One may then apply ideas from calculus while working within the individual charts, since each chart lies within a vector space to which the usual rules of calculus apply. If the charts are suitably compatible (namely, the transition from one chart to another is differentiable), then computations done in one chart are valid in any other differentiable chart.
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