What is the Difference Between Local and Global Maximum?

The difference between local and global maximum lies in the scope of their application within a function.

• Local Maximum: This refers to the largest value in a subset of the function within a specific range. A function can have multiple local maxima, as there can be several points within the function that achieve the largest value in their respective regions.
• Global Maximum: This refers to the largest value in the entire function over its entire domain. There can only be a single global maximum for each function, as it represents the highest value achieved by the function across all points in its domain.

In the context of product management, local maxima can represent the biggest potential impact you can make in a specific area, while the global maximum represents the highest overall impact. It is essential to continuously assess whether you are chasing your global maximum or optimizing for your local maximum, as focusing solely on one can lead to missed opportunities for greater impact.

Comparative Table: Local vs Global Maximum

The difference between local and global maxima can be understood through the following table:

In summary, a local maximum is the largest value in a specific region of a function, while a global maximum is the largest value in the entire function. Local maxima can be multiple, whereas there is only one global maximum for each function. Understanding the difference between local and global maxima can help in identifying the most impactful opportunities and making better decisions in various fields, including product management.