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

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