Local extrema focuses on small intervals, and absolute extrema considers the function's entire domain, making them global characteristics of the function.
Absolute extrema vs local extrema
The absolute maximum and minimum, akin to local extrema, pinpoint significant points on a function where extreme values are reached.
Shared characteristics include their association with critical points, where the derivative is zero or undefined. However, distinctions arise in their scope and identification.
Local extrema are confined to specific intervals and are determined by examining the function's behavior around critical points. In contrast, absolute extrema considers the entire function domain, necessitating a global analysis.
Unlike local extrema, absolute extrema may not exist for some functions. Hence, these mathematical concepts offer insights into both local and global behaviors of functions.