Relative extrema (relative minimum and maximum)

Relative extrema, or relative minimums and maximums of a function, or of its graph, are points in its domain (where it's graph exists) where the function has the highest or lowest value for a small region around that point.

For example, the following graph has relative extrema at x = 0.11 and x = 1

Relative extrema of a function can be calculated by the help of its critical points. This is because the relative extrema always exist only at critical points. That is, only a critical point of a function can be its relative maximum or minimum

Critical points need to be classified as relative minimums and maximums. There are three ways to do this:

• Check function's value at and between the critical points
• First derivative test
• Second derivative test