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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
The critical point is described by a conformal field theory. According to the renormalization group theory, the defining property of criticality is that the characteristic length scale of the structure of the physical system, also known as the correlation length ξ, becomes infinite. This can happen along critical lines in phase space.
The definition of global minimum point also proceeds similarly. If the domain X is a metric space, then f is said to have a local (or relative) maximum point at the point x ∗, if there exists some ε > 0 such that f(x ∗) ≥ f(x) for all x in X within distance ε of x ∗.
At the remaining critical point (0, 0) the second derivative test is insufficient, and one must use higher order tests or other tools to determine the behavior of the function at this point. (In fact, one can show that f takes both positive and negative values in small neighborhoods around (0, 0) and so this point is a saddle point of f.)
The point at the very top of the dome is called the critical point. This point is where the saturated liquid and saturated vapor lines meet. Past this point, it is impossible for a liquid–vapor transformation to occur. [3] It is also where the critical temperature and critical pressure meet.
Critical value or threshold value can refer to: A quantitative threshold in medicine, chemistry and physics; Critical value (statistics), boundary of the acceptance region while testing a statistical hypothesis; Value of a function at a critical point (mathematics) Critical point (thermodynamics) of a statistical system.