Local minima 

Local Minima

In optimization and mathematical analysis, a local minimum refers to a point in a function's domain where the function's value is lower than the values of nearby points, but not necessarily the lowest value that the function can achieve globally.

Here are some key points about local minima:

1. Definition: A point \(x\) is considered a local minimum of a function \(f(x)\) if there exists an open interval around \(x\) such that \(f(x)\) is less than or equal to \(f(y)\) for all \(y\) within that interval.

2. Critical Points: Local minima often occur at critical points of a function, where the ____ ______ ________ ____ ______ _________ _______ _________ ____ ______ ______ _________.
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