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  2. Maximum and minimum - Wikipedia

    en.wikipedia.org/wiki/Maximum_and_minimum

    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 domain. So a method of finding a global maximum (or minimum) is to look at all the local maxima (or minima) in the interior, and also look at the maxima (or minima) of the points on the ...

  3. Extreme value theorem - Wikipedia

    en.wikipedia.org/wiki/Extreme_value_theorem

    A continuous function () on the closed interval [,] showing the absolute max (red) and the absolute min (blue).. In calculus, the extreme value theorem states that if a real-valued function is continuous on the closed and bounded interval [,], then must attain a maximum and a minimum, each at least once.

  4. Derivative test - Wikipedia

    en.wikipedia.org/wiki/Derivative_test

    The first-derivative test is helpful in solving optimization problems in physics, economics, and engineering. In conjunction with the extreme value theorem, it can be used to find the absolute maximum and minimum of a real-valued function defined on a closed and bounded interval.

  5. Calculus of variations - Wikipedia

    en.wikipedia.org/wiki/Calculus_of_Variations

    The calculus of variations may be said to begin with Newton's minimal resistance problem in 1687, followed by the brachistochrone curve problem raised by Johann Bernoulli (1696). [2] It immediately occupied the attention of Jacob Bernoulli and the Marquis de l'Hôpital , but Leonhard Euler first elaborated the subject, beginning in 1733.

  6. Newton's method - Wikipedia

    en.wikipedia.org/wiki/Newton's_method

    Newton's method can be used to find a minimum or maximum of a function f(x). The derivative is zero at a minimum or maximum, so local minima and maxima can be found by applying Newton's method to the derivative. [37] The iteration becomes: + = ′ ″ ().

  7. Adequality - Wikipedia

    en.wikipedia.org/wiki/Adequality

    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.

  8. Second partial derivative test - Wikipedia

    en.wikipedia.org/wiki/Second_partial_derivative_test

    If D(a, b) = 0 then the point (a, b) could be any of a minimum, maximum, or saddle point (that is, the test is inconclusive). Sometimes other equivalent versions of the test are used. In cases 1 and 2, the requirement that f xx f yy − f xy 2 is positive at ( x , y ) implies that f xx and f yy have the same sign there.

  9. Newton's method in optimization - Wikipedia

    en.wikipedia.org/wiki/Newton's_method_in...

    The geometric interpretation of Newton's method is that at each iteration, it amounts to the fitting of a parabola to the graph of () at the trial value , having the same slope and curvature as the graph at that point, and then proceeding to the maximum or minimum of that parabola (in higher dimensions, this may also be a saddle point), see below.

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