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A critical point of a function of a single real variable, f (x), is a value x 0 in the domain of f where f is not differentiable or its derivative is 0 (i.e. ′ =). [2] A critical value is the image under f of a critical point.
In thermodynamics, a critical point (or critical state) is the end point of a phase equilibrium curve. One example is the liquid–vapor critical point, the end point of the pressure–temperature curve that designates conditions under which a liquid and its vapor can coexist.
Critical point may refer to: Critical phenomena in physics; Critical point (mathematics), in calculus, a point where a function's derivative is either zero or nonexistent; Critical point (set theory), an elementary embedding of a transitive class into another transitive class which is the smallest ordinal which is not mapped to itself
A saddle point (in red) on the graph of z = x 2 − y 2 (hyperbolic paraboloid). In mathematics, a saddle point or minimax point [1] is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a critical point), but which is not a local extremum of the function. [2]
A turning point of a differentiable function is a point at which the derivative has an isolated zero and changes sign at the point. [2] A turning point may be either a relative maximum or a relative minimum (also known as local minimum and maximum). A turning point is thus a stationary point, but not all stationary points are turning points.
Critical thinking, in education; Criticality index, in risk analysis; Criticality matrix, a representation (often graphical) of failure modes along with their probabilities and severities; Self-organized criticality, a property of (classes of) dynamical systems which have a critical point as an attractor
A word of warning: some authors use the term critical point to describe a point where the rank of the Jacobian matrix of f at p is not maximal. [2] Indeed, this is the more useful notion in singularity theory. If the dimension of M is greater than or equal to the dimension of N then these two notions of
The concept of a single point of failure has also been applied to fields outside of engineering, computers, and networking, such as corporate supply chain management [6] and transportation management. [7] Design structures that create single points of failure include bottlenecks and series circuits (in contrast to parallel circuits).