# What are extrema?

May 18, 2015

Maximum = maximum value = greatest $y$ value (locally or globally)

(The first "maximum" here is a noun, the second is an adjective modifying "value".)

Minimum = minimum value = least $y$ value (locally or globally)

Two maximum value = two maxima (Latin plural of maximum)

Two minimum values = two minima (Latin plural of minimum)

Extreme value = minimum or maximum value.

Two extreme values = two extrema (Latin plural of extremum).

Example:

The function shown below has two local minima and one local maximum, for a total of 3 local extrema.

It has one global minimum.

(Instead of "local" and "global" you may also see/hear "relative" and "absolute".)

graph{ (x+2)(x-3)(x-5)(x-8)/80 [-11.7, 16.79, -8.7, 5.53]}