Local maxima are points in a function where the function value is higher than all nearby points, representing a peak in the function's graph. They are crucial in optimization problems, helping to identify optimal solutions within a specific region of the domain, but may not represent the absolute highest point of the entire function, known as the global maximum.

Local Maxima

Local maxima

points in a function

function value

nearby points

peak in the function's graph

Optimization problems involve finding the best solution from a set of feasible solutions, often under given constraints. They are fundamental in various fields such as operations research, economics, and computer science, where the goal is to maximize or minimize an objective function.

optimization problems

optimal solutions

specific region of the domain

absolute highest point

A global maximum is the highest point over the entire domain of a function, representing the largest value the function can achieve. It is crucial in optimization problems where the goal is to find the most optimal solution among all possible solutions.

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