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A critical point of a function of a single real variable, f (x), is a value x0 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. These concepts may be visualized through the graph of f: at a critical point, the graph has a horizontal tangent if one can ...
Symbolab. Symbolab is an answer engine [ 1] that provides step-by-step solutions to mathematical problems in a range of subjects. [ 2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero ...
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. At higher temperatures, the gas comes into a supercritical phase ...
The absolute value of a number may be thought of as its distance from zero. In mathematics, the absolute value or modulus of a real number , denoted , is the non-negative value of without regard to its sign. Namely, if is a positive number, and if is negative (in which case negating makes positive), and . For example, the absolute value of 3 is ...
The Taylor series can be used to calculate the value of an entire function at every point, if the value of the function, and of all of its derivatives, are known at a single point. Uses of the Taylor series for analytic functions include: The partial sums (the Taylor polynomials) of the series can be used as approximations of the function ...
Equilibrium point (mathematics) Stability diagram classifying Poincaré maps of linear autonomous system as stable or unstable according to their features. Stability generally increases to the left of the diagram. [ 1] Some sink, source or node are equilibrium points. In mathematics, specifically in differential equations, an equilibrium point ...
Critical exponent. Critical exponents describe the behavior of physical quantities near continuous phase transitions. It is believed, though not proven, that they are universal, i.e. they do not depend on the details of the physical system, but only on some of its general features. For instance, for ferromagnetic systems at thermal equilibrium ...
A statistical hypothesis test typically involves a calculation of a test statistic. Then a decision is made, either by comparing the test statistic to a critical value or equivalently by evaluating a p -value computed from the test statistic. Roughly 100 specialized statistical tests have been defined. [ 1 ][ 2 ]