Absolute Maxima and Minima
1. What is Absolute Maxima of the Function?
The maximum value of the function over its entire domain is called the Absolute maxima of the function. Suppose we are given a function f(x) = 2x2 then its domain is R and its maximum value is ∞ at x –> ∞. Thus, its Absolute maxima is ∞.
2. What is Absolute Minima of the Function?
The minimum value of the function over its entire domain is called the Absolute minima of the function. Suppose we are given a function f(x) = 2x2 then its domain is R and its minimum value is 0 at x = 0. Thus, its Absolute minima is 0.
3. What are the Conditions for Absolute Maxima and Minima?
The absolute maxima and minima of a function {say f(x)} occur at critical points and endpoints within a given interval.
4. How to Find the Absolute Maxima and Minima?
To find the absolute maxima and minima of the given function follow the following steps.
Step 1: Differentiate the given function f(x) to f'(x)
Step 2: Equate the f'(x) to zero to get the critical points of the function.
Step 3: Find the value of the function f(x) at all critical points and at the end points of the given interval.
Step 4: Comapare all the values of f(x) to find the required value of Absolute Maxima and Absolute Minima.
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?