Use the input boxes to define a function f(x) on an interval [a, b]. Use the checkboxes for a and b to include/exclude the endpoints of the interval. Use the checkboxes to show/hide interior extreme values, critical points, intervals of increase/decrease (monotonicity), and the graph of the derivative function.

The first derivative can tell us where a function is increasing or decreasing. [br][list][*]f is increasing wherever f' is positive[/*][*]f is decreasing wherever f' is negative[/*][/list][br]The first derivative test gives us a way to test critical points to determine if there is an extreme value there. [br][list][*]A function has a local maximum at a critical point c if f changes from increasing to decreasing at c (i.e., if f' changes from positive to negative). [/*][*]A function has a local minimum at a critical point c if f changes from decreasing to increasing at c (i.e., if f' changes from negative to positive). [/*][/list]