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Finding global maxima and minima is the goal of mathematical optimization. If a function is continuous on a closed interval, then by the extreme value theorem, global maxima and minima exist. Furthermore, a global maximum (or minimum) either must be a local maximum (or minimum) in the interior of the domain, or must lie on the boundary of the ...
Adequality is a technique developed by Pierre de Fermat in his treatise Methodus ad disquirendam maximam et minimam [1] (a Latin treatise circulated in France c. 1636 ) to calculate maxima and minima of functions, tangents to curves, area, center of mass, least action, and other problems in calculus.
His book, Treatise on Problems of Maxima and Minima, was promoted by mathematician Augustus De Morgan. Writing in his preface to the treatise, De Morgan states that Ramchundra was born in about 1821 in Panipat to Sunder Lal, a Kayasth of Delhi. He came to De Morgan’s attention when, in 1850, a friend sent him Ramchundra’s work on maxima and ...
The problem of finding the local maxima and minima subject to constraints can be generalized to finding local maxima and minima on a differentiable manifold . [14] In what follows, it is not necessary that be a Euclidean space, or even a Riemannian manifold.
Maxima and minima; First derivative test; Second derivative test; Extreme value theorem; Differential equation; Differential operator; Newton's method; Taylor's theorem; L'Hôpital's rule; General Leibniz rule; Mean value theorem; Logarithmic derivative; Differential (calculus) Related rates; Regiomontanus' angle maximization problem; Rolle's ...
In numerical analysis, a quasi-Newton method is an iterative numerical method used either to find zeroes or to find local maxima and minima of functions via an iterative recurrence formula much like the one for Newton's method, except using approximations of the derivatives of the functions in place of exact derivatives.
Fermat's theorem is central to the calculus method of determining maxima and minima: in one dimension, one can find extrema by simply computing the stationary points (by computing the zeros of the derivative), the non-differentiable points, and the boundary points, and then investigating this set to determine the extrema.
Finding the extrema of functionals is similar to finding the maxima and minima of functions. The maxima and minima of a function may be located by finding the points where its derivative vanishes (i.e., is equal to zero). The extrema of functionals may be obtained by finding functions for which the functional derivative is equal to zero.
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