Monotonicityof a function
Task
Graph the derivative of a function to observe the monotonicity.
Explore the construction and learn how to create an applet for exploring the monotony with respect to the derivative of a function with GeoGebra Graphing Calculator. Then try it yourself by following the instructions below.
Explore the construction...
Instructions
| 1. | | Enter into the Input Bar. |
| 2. | | Enter into the Input Bar to graph the derivative of f(x). |
| 3. | | Use the command to show the coordinates of the extrema of f(x) as well as to display the points in the Graphics View. |
| 4. | | Enter to color the area for which the derivative of f(x) is positive. |
| 5. | | Enter to color the area for which the derivative of f(x) is negative. |
| 6. |   | Enhance your construction by chanigng the line thickness and color of the graphs and areas using the Style Bar of the selected object. |
| 7. | | Observe the relation of f'(x) and the monotonicity of f(x). |