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The extreme value theorem was originally proven by Bernard Bolzano in the 1830s in a work Function Theory but the work remained unpublished until 1930. Bolzano's proof consisted of showing that a continuous function on a closed interval was bounded, and then showing that the function attained a maximum and a minimum value.
Extreme value theory or extreme value analysis (EVA) is the study of extremes in statistical distributions. It is widely used in many disciplines, such as structural engineering , finance , economics , earth sciences , traffic prediction, and geological engineering .
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 theorem
Pages in category "Theorems in calculus" The following 38 pages are in this category, out of 38 total. ... Extreme value theorem; F. Fermat's theorem (stationary points)
For example, if a bounded differentiable function f defined on a closed interval in the real line has a single critical point, which is a local minimum, then it is also a global minimum (use the intermediate value theorem and Rolle's theorem to prove this by contradiction). In two and more dimensions, this argument fails.
Extreme value theorem [ edit ] The extreme value theorem states that if a function f is defined on a closed interval [ a , b ] {\displaystyle [a,b]} (or any closed and bounded set) and is continuous there, then the function attains its maximum, i.e. there exists c ∈ [ a , b ] {\displaystyle c\in [a,b]} with f ( c ) ≥ f ( x ) {\displaystyle ...
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.
13 Extreme value theorem. ... In mathematics, nonstandard calculus is the modern application of infinitesimals, ... Example 1: a function f is ...
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