Relative Minimums and Maximums

Definition

Relative minimums and maximums are points on a graph where a function reaches its lowest or highest value within a specific interval. A relative minimum occurs when there is a downward shift in direction from both sides of the point, while a relative maximum occurs when there is an upward shift in direction.

Related terms

Critical Points:

Critical points are locations on a graph where either the derivative is zero or does not exist. They can correspond to relative minimums/maximums or other important features.

Concavity:

Concavity refers to whether a curve is bending upwards (concave up) or downwards (concave down). It helps determine the presence of relative minimums/maximums.

Inflection Points:

Inflection points are points on a graph where the concavity changes. They do not necessarily correspond to relative minimums/maximums, but they indicate a change in curvature.