## GeoGebra Tutorial 17 – Functions, Tangent Lines and Derivatives

This is the 17th tutorial of the GeoGebra Intermediate Tutorial Series. If this is your first time to use GeoGebra, I strongly suggest that you read the GeoGebra Essentials Series.    In this tutorial, we are going to use slider control a, b, c, d and e and graph the function f(x) = ax4 + bx3 + cx2 + dx + e.

Figure 1

We then  construct a line tangent to the function and passing through  point A and trace the graph of the point whose x-coordinate is the x-coordinate of A, and whose y-coordinate as the  slope of the tangent line. We compute for the derivative of f(x), and see if  there is a relationship between the trace and the derivative. If you want to follow the this tutorial step by step, you can open the GeoGebra window. Before following the tutorial, you may want to see the final output.

## GeoGebra Basic Construction 5– Rectangle

In this GeoGebra tutorial, we use the Perpendicular Line and Parallel Line tools to construct a rectangle. The idea is to construct segment AB, construct two lines perpendicular to it, one passing through segment A and the other through segment B. Next, we will construct point on the line passing through B, then construct a line parallel to AB passing through C. The fourth intersection will be our point D. If you want to follow this construction step-by-step, click here to open GeoGebra on your browser.

Step-by-Step Construction

 1. Open GeoGebra and select Geometry from the Perspective menu on the side bar. 2. To automatically show the labels of points and not the other objects, click the Options menu, click Labeling, then click New Points Only. 3. To construct a rectangle, select the Segment between Two Points tool and click two distinct places on the Graphics view to construct segment AB. 4. We construct two lines that are both perpendicular to AB, one passing through A and the other through B. To do this, click the Perpendicular Line tool, click point A and click the segment. To construct another line, click point B then click the segment. After these steps, your drawing should look like the one shown in Figure 1. Figure 1 5. Next, we construct a point on the line passing through point B. To do this, click the New Point tool, and then click on the line passing through B. 6. Now, to create a line parallel to AB, passing through point C, click the Parallel line tool, click on point C and then click on the segment. Figure 2 Your drawing should look like the one shown in Figure 2 after this step. 7. Using the intersect tool, we construct the intersection of the line passing C (parallel to AB) and the line passing through A. To do this, click the Intersect Two Objects tool and click the two lines mentioned. 8. Now, we hide the three lines. To do this, click the Show/Hide Object tool and click the three lines. Notice that the lines are highlighted. Click Move tool to hide the lines. 9. Use the Segment between Two Points tool to connect the points to construct the rectangle. 10.  Drag the points of the vertices of the rectangle. What do you observe?

## Invitation to the Mathematics and Multimedia Blog Carnival

Hi guys. I am happy to announce that I will be hosting my own blog carnival — the Mathematics and Multimedia Blog Carnival. M&M Carnival will include K-12  topics in mathematics. Although, any math  topic is allowed, the following topics will be prioritized:

1. connections between and among different topics in mathematics as well connection of mathematics to other fields
2. use of mathematics in solving real life problems
3. clear, non-bookish conceptual explanations of mathematical concepts, particularly those which are hard to teach and difficult to learn
4. integration of technology in teaching mathematics
5. introduction of new software and Web 2.0 technologies
6. software reviews and tutorials