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Absolute minimum:

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It is the smallest function value on the entire domain of the function

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Local minimum at \"\":

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It is the smallest function value when \"\" is near to \"\".

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There can be many local minimum points but there is one absolute minimum point for a function.

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An local minimum can be absolute maximum but a absolute maximum cannot be local minimum.

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An local minimum can be absolute maximum but a absolute maximum cannot be local minimum.