Absolute Min and Max

The absolute extrema of a function on a closed interval is either a local extrema or a boundary point. In this applet there is a continuous function defined by the black dots. Adjusting the dots will modify the function. The closed interval boundary is adjustable with the orange plus symbols on the x-axis. The end points of the function are shown as orange circles and the interval is grayed. Checking "Local Extrema" will put a dark green plus on local minimum and maximum values. Checking "Extreme Values" will show the absolute maximum and minimum values in the closed interval. 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. Draw a graph of a function with a local maximum where the derivative is not zero. Change the boundaries and watch how the minimum and maximum values change.