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Illustrated definition of Maximum: The largest value. The maximum of 14, 4, 16, 12 is 16. Try it yourself below:
- Minimum
Illustrated definition of Minimum: The smallest value. The...
- Minimum
Mathematics defines a maximum as the highest value of a set. In other words, it is the highest value that a certain quantity can attain . The concept of maximum is often used in optimization problems where the goal is to find the best solution given certain constraints.
- Local Maximum and Minimum
- Local Maximum
- Global (or Absolute) Maximum and Minimum
Functions can have "hills and valleys": places where they reach a minimum or maximum value. It may not be the minimum or maximum for the whole function, but locallyit is. We can see where they are, but how do we define them?
Firstwe need to choose an interval: Then we can say that a local maximumis the point where: Or, more briefly: f(a) ≥ f(x) for all x in the interval In other words, there is no height greater than f(a). Note: "a" should be insidethe interval, not at one end or the other.
The maximum or minimum over the entire functionis called an "Absolute" or "Global" maximum or minimum. Assumingthis function continues downwards to left or right: 1. The Global Maximum is about 3.7 2. There is no Global Minimum (as the function extends infinitely downwards)
Aug 21, 2011 · You can define like that the maximum of any finitely many elements. When the parameters are an infinite set of values, then it is implied that one of them is maximal (namely that there is a greatest one, unlike the set $\{-\frac{1}{n} | n\in\mathbb{N}\}$ where there is no greatest element)
A maximum (plural maxima), in the context of functions, is the largest value of the function either within a given interval, or over the entire domain of the function. In other words, a point on a function is a maximum if its height is greater than or equal to any other point within the given interval.
In mathematical analysis, the maximum and minimum[a] of a function are, respectively, the greatest and least value taken by the function.
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Nov 26, 2024 · The maximum value of a set of elements A={a_i}_(i=1)^N is denoted maxA or max_(i)a_i, and is equal to the last element of a sorted (i.e., ordered) version of A. For example, given the set {3,5,4,1}, the sorted version is {1,3,4,5}, so the maximum is 5.
