Extrema or extreme values
The maximum and minimum values of a function
Extrema or extreme values refer to the highest and lowest points of a function or data set. A function may have one or more extrema, called local extrema, depending on its behavior.
To find the extrema, we need to take the derivative of the function and set it equal to zero. This gives us the critical points, which we can then evaluate to determine if they are maximum, minimum, or neither.
There are two types of extrema: relative and absolute. Relative extrema are local extrema that occur only within a specific range of the function, while absolute extrema are the highest and lowest values of the function over its entire domain.
In practical applications, finding extrema is important for optimizing processes, such as finding the maximum profit or minimum cost of production.
Overall, understanding extrema is an essential concept in calculus and is considered one of the fundamental techniques in solving optimization problems.
More Answers:
How to Find the Absolute Maximum of a Function – A Guide for Math EnthusiastsThe Extreme Value Theorem: Finding Optimal Solutions in Calculus and Mathematical Modeling.
Discovering Endpoint Extrema: A Guide to Understanding the Significance of Minimum and Maximum Values in Real-World Applications