5-B First Derivative Test
Instructions
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.
5-B First Derivatives and Monotonicity
The first derivative can tell us where a function is increasing or decreasing.
- f is increasing wherever f' is positive
- f is decreasing wherever f' is negative
- 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).