Extrema Value Theorem
Extrema value theorem guarantees both the maxima and minima for a function under certain conditions. This theorem does not tell us where the extreme points will exist, this theorem tells us only that extreme value will exist. The theorem states that,
If a function f(x) is continuous on a closed interval [a, b], then f(x) has both at least one maximum and minimum value on [a, b].
Absolute Minima and Maxima
Absolute Maxima and Minima are the maximum and minimum values of the function defined on a fixed interval. A function in general can have high values or low values as we move along the function. The maximum value of the function in any interval is called the maxima and the minimum value of the function is called the minima. These maxima and minima if defined on the whole functions are called the Absolute Maxima and Absolute Minima of the function.
In this article, we will learn about Absolute Maxima and Mimima, How to calculate absolute maxima and minima, their examples, and others in detail.
Table of Content
- What are Absolute Maxima and Minima?
- Critical Points and Extrema Value Theorem
- Extrema Value Theorem
- Absolute Minima and Maxima in Closed Interval
- Absolute Minima and Maxima in Entire Domain
- What are Local Maxima and Minima?
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