Relative Maxima and Minima
The relative maxima or relative minima is the maximum and minimum value which is greater than or lesser than its neighbor.
Relative Maxima
A function f(x) is said to have a relative maximum at x = a if there exists a neighborhood (a – δa, a + δa) of a such that
f(x) < f(a) for all x ∈ (a-δa, a+δa), x ≠ a.
Here, the point a is called the point of relative maxima of a function and f(a) is called as the relative maximum value. The relative maxima is also called as the local maxima of a function.
Relative Minima
A function f(x) is said to have a relative minimum at x = a if there exists a neighborhood (a-δa, a+δa) of a such that
f(x) > f(a) for all x ∈ (a-δa, a+δa), x ≠ a.
Here, the point a is called the point of minima of a function and f(a) is called as the relative minimum value. The relative minima is also called as the local minima of a function. In the article linked below we can learn how to find relative maxima and minima.
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Maxima and Minima in Calculus
Maxima and Minima in Calculus is an important application of derivatives. The Maxima and Minima of a function are the points that give the maximum and minimum values of the function within the given range. Maxima and minima are called the extremum points of a function.
This article explores the concept of maxima and minima. In addition to details about maxima and minima, we will also cover the types of maxima and minima, properties of Maxima and Minima, provide examples of maxima and minima, and discuss applications of Maxima and Minima.
Table of Content
- Maxima and Minima of a Function
- Types of Maxima and Minima
- Relative Maxima and Minima
- Absolute Maxima and Minima
- How to Find Maxima and Minima?
- Applications of Maxima and Minima
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