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.