What are Maxima and Minima of a Function?
The maxima and minima are the most used applications of the derivatives. The maxima and minima provide us with the peaks and valleys of a function. Below we will discuss the maxima and minima of the function in depth and explore the different types of maxima and minima.
Read in Detail: Calculus in Maths
Maxima Definition
Let f(x) be a real function defined on an interval I then, f(x) is said to have the maximum value in I, if there exists a point ‘a’ in I such that f(x) ≤ f(a) for all x ∈ I.
The number f(a) is called the maximum value of f(x) in the interval I and point a is called the point of maxima of f in interval I. The maxima of a function are defined as the point in the given interval where the function value is maximum. In other words, maxima is the highest point on the curve of a function. There are two types of maxima:
- Local or Relative Maxima
- Absolute or Global Maxima
Minima Definition
Let f(x) be a real function defined on an interval I then, f(x) is said to have the minimum value in I, if there exists a point ‘a’ in I such that f(x) ≥ f(a) for all x ∈ I.
The number f(a) is called the minimum value of f(x) in interval I and the point a is called the point of minima of f in the interval I. The minima of a function is defined as the point in the given interval where the function value is minimum. In other words, minima is the lowest point on the curve of a function.
There are two types of minima:
- Relative or Local Minima
- Absolute or Global Minima
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