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  2. Maximum and minimum - Wikipedia

    en.wikipedia.org/wiki/Maximum_and_minimum

    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 ...

  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 f {\displaystyle f} is continuous on the closed and bounded interval [ a , b ] {\displaystyle [a,b]} , then f {\displaystyle f} must attain a maximum and a ...

  4. Derivative test - Wikipedia

    en.wikipedia.org/wiki/Derivative_test

    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. In conjunction with other information such as concavity, inflection points, and asymptotes , it can be used to sketch the graph of a function.

  5. Maximal and minimal elements - Wikipedia

    en.wikipedia.org/wiki/Maximal_and_minimal_elements

    The maximum of a subset of a preordered set is an element of which is greater than or equal to any other element of , and the minimum of is again defined dually. In the particular case of a partially ordered set , while there can be at most one maximum and at most one minimum there may be multiple maximal or minimal elements.

  6. Sample maximum and minimum - Wikipedia

    en.wikipedia.org/wiki/Sample_maximum_and_minimum

    The minimum and the maximum value are the first and last order statistics (often denoted X (1) and X (n) respectively, for a sample size of n). If the sample has outliers, they necessarily include the sample maximum or sample minimum, or both, depending on whether they are extremely high or low. However, the sample maximum and minimum need not ...

  7. Stationary point - Wikipedia

    en.wikipedia.org/wiki/Stationary_point

    The stationary points are the red circles. In this graph, they are all relative maxima or relative minima. The blue squares are inflection points.. In mathematics, particularly in calculus, a stationary point of a differentiable function of one variable is a point on the graph of the function where the function's derivative is zero.

  8. Box plot - Wikipedia

    en.wikipedia.org/wiki/Box_plot

    Box-plot with whiskers from minimum to maximum Figure 3. Same box-plot with whiskers drawn within the 1.5 IQR value Same box-plot with whiskers drawn within the 1.5 IQR value A boxplot is a standardized way of displaying the dataset based on the five-number summary : the minimum, the maximum, the sample median, and the first and third quartiles.

  9. Golden-section search - Wikipedia

    en.wikipedia.org/wiki/Golden-section_search

    The golden-section search is a technique for finding an extremum (minimum or maximum) of a function inside a specified interval. For a strictly unimodal function with an extremum inside the interval, it will find that extremum, while for an interval containing multiple extrema (possibly including the interval boundaries), it will converge to one of them.