Concept

Relative Minimum and Maximum

The value f(c) is a relative minimum, or local minimum, of a function if f(c) is the least output of f around x=c. Likewise, the value f(d) is a relative maximum, or local maximum, of a function if f(d) is the greatest output of f around x=d.
Relative extrema of a cubic function
If the function is continuous, the function switches from increasing to decreasing at a relative maximum or from decreasing to increasing at a relative minimum.
Sometimes the phrase relative extrema is used to refer to both relative maximums and relative minimums. Note that a function can have one or more relative extrema, or none at all.
Exercises