What is Global Maxima and Minima?

The global maxima also called the absolute maxima is the highest value in the entire domain of the function. The global minima also called the absolute minima is the lowest value in the entire domain of the function.

Global Maxima Definition

A function f(x) with domain D is called global maximum at x = a where a ∈ D, if f(x) ≤ f(a) for all x ∈ D. The point a is called the point of global maxima of the function and f(a) is called as the global maximum value.

Condition for Global Maxima

Condition for global maxima is given by:

x = a is point of global maxima when

f(x) ≤ f(a) for all x ∈ D

f(a) is called the global maximum value.

Global Minima Definition

A function f(x) with domain D is called global minimum at x = a where a ∈ D, if f(x) ≥ f(a) for all x ∈ D. The point a is called the point of global minima of the function and f(a) is called as the global minimum value for global minima.

Condition for Global Minima

Condition for global minima is given by:

x = a is point of global minima when

f(x) ≥ f(a) for all x ∈ D

f(a) is called the global minimum value.

Do you ever wonder how to find the highest or lowest points of something? Maybe you’re trying to figure out the best temperature for baking cookies or the shortest route to school. In the world of mathematics, we call these high points “global maximums” and low points “global minimums.” They’re like the peaks and valleys of a roller coaster, showing us the highest and lowest points along the ride.

In this article, we’ll take a journey into the world of finding global maximums and minimums.