The absolute extrema of a function on a closed interval is either a local extrema or a boundary point.[br]In this applet there is a continuous function defined by the black dots. Adjusting the dots will modify the function.[br]The closed interval boundary is adjustable with the orange plus symbols on the x-axis.[br]The end points of the function are shown as orange circles and the interval is grayed.[br]Checking "Local Extrema" will put a dark green plus on local minimum and maximum values.[br]Checking "Extreme Values" will show the absolute maximum and minimum values in the closed interval.[br]Checking "Box" will draw a box to show that the function does not exceed the maximum value or fall below the minimum value within the interval.

A local extrema can occur anywhere the function derivative is zero or undefined.[br]Draw a graph of a function with a local maximum where the derivative is not zero.[br][br]Change the boundaries and watch how the minimum and maximum values change.