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The inflection point at which the increase in response with increasing ligand concentration begins to slow is the EC 50, which can be mathematically determined by derivation of the best-fit line. While relying on a graph for estimation is more convenient, this typical method yields less accurate and precise results.
A rising point of inflection is a point where the derivative is positive on both sides of the point; in other words, it is an inflection point near which the function is increasing. For a smooth curve given by parametric equations , a point is an inflection point if its signed curvature changes from plus to minus or from minus to plus, i.e ...
The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.
A sigmoid function is a bounded, differentiable, real function that is defined for all real input values and has a non-negative derivative at each point [1] [2] and exactly one inflection point. Properties
Low-order polynomials tend to be smooth and high order polynomial curves tend to be "lumpy". To define this more precisely, the maximum number of inflection points possible in a polynomial curve is n-2, where n is the order of the polynomial equation. An inflection point is a location on the curve where it switches from a positive radius to ...
The Gompertz curve or Gompertz function is a type of mathematical model for a time series, named after Benjamin Gompertz (1779–1865). It is a sigmoid function which describes growth as being slowest at the start and end of a given time period.
The parameters of the dose response curve reflect measures of potency (such as EC50, IC50, ED50, etc.) and measures of efficacy (such as tissue, cell or population response). A commonly used dose–response curve is the EC 50 curve, the half maximal effective concentration, where the EC 50 point is defined as the inflection point of the curve.
Points where concavity changes (between concave and convex) are inflection points. [5] If f is twice-differentiable, then f is concave if and only if f ′′ is non-positive (or, informally, if the "acceleration" is non-positive). If f ′′ is negative then f is strictly concave, but the converse is not true, as shown by f(x) = −x 4.