Explain The Difference Between An Absolute Minimum And A Local Minimum.

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Explain the difference between an absolute minimum and a local minimum.

Answer

Local minimum is the smallest value that a function has on some open interval (which is part of domain).

Absolute minimum is the smallest value that a function has on its entire domain.

Note:

Local minimum can be reached in just one point.

There is just one absolute minimum, but it can be reached in multiple point.

explain the difference between an absolute minimum and a local minimum.

For example: f(x) = x^4 + x^3 – x^2

A point A is an absolute minimum, also A is local minimum.

A point C is only a local minimum.

The points that are at the end of the graph can never be the local minimum, because there is no open interval around the end point.

Result

Local minimum is the smallest value that a function has on some open interval (which is part of domain).

Absolute minimum is the smallest value that a function has on its entire domain.

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