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# Minimums and Maximums

## Highest or lowest y values within an area or function.

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Maximums and Minimums

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### Vocabulary Language: English

absolute extrema

The absolute extrema of a function are the points with the $y$ values that are the highest or the lowest of the entire function.

End behavior

End behavior is a description of the trend of a function as input values become very large or very small, represented as the 'ends' of a graphed function.

Function

A function is a relation where there is only one output for every input. In other words, for every value of $x$, there is only one value for $y$.

global extrema

The global extrema of a function are the points with the $y$ values that are the highest or the lowest of the entire function.

local extrema

The local extrema of a function are the points of the function with $y$ values that are the highest or lowest of a local neighborhood of the function.

Local Maximum

A local maximum is the highest point relative to the points around it. A function can have more than one local maximum.

Local Minimum

A local minimum is the lowest point relative to the points around it. A function can have more than one local minimum.

Maximum

The maximum is the highest point of a graph. The maximum will yield the largest value of the range.

Minimum

The minimum is the lowest point of a graph. The minimum will yield the smallest value of the range.

relative extrema

The relative extrema of a function are the points of the function with $y$ values that are the highest or lowest of a local neighborhood of the function.