5-A Extreme Values & Critical Points
Instructions
Use the input boxes below to define a function f(x) on an interval [a,b]. Use the checkboxes for a and b to exclude the endpoints from the domain of the function. Use the checkboxes to show/hide the critical points and local extrema in the interior of the interval (i.e., not at the endpoints). Use the "Trace y" button to trace points on the y-axis as you move the point c across the domain.
5-A Extreme Values & Critical Points
When we talk about extreme values of a function, we mean maximum or minimum values (without specifying which type).
Global (Absolute) Extreme Values:
- f has a global maximum at x=c if for all x in the domain of f.
- f has a global minimum at x=c if for all x in the domain of f.
- f has a local maximum at x=c if for all x in an interval containing x = c.
- f has a local minimum at x=c if for all x in an interval containing x = c.