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Graphs and Their Properties

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)



Questions:
1.)   Which interval/s of the function f is/are increasing? is/are decreasing?
2.)   What is the relationship between the critical points of the graph (maximum, minimum, point of inflection) to the function to its derivative?
3.)   What is the relationship between critical points and the slope of the tangent line?

The Geometry of Derivative

Move point Q towards point P.


This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com


As Q approaches P,

1.) What do you observe about the inclination of the secant line in relation to the inclination of the tangent line?
2.) What do observe about the value of h?
3.) What do you observe about the value of the slope of the secant line?
4.) What happens to the value of h and the slope of the tangent line if Q coincides with P?

Plotting Points Exercise

Drag the points to their appropriate coordinate. Reload your page to get another set of points.




















This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Tracing the Ellipse

1. Move slider r to trace the ellipse.
2. You can choose to show/hide the circles using the Show Circles check box.
3. Use the tools available in the toolbar to explore the properties of the ellipse formed.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

I will construct a step-by-step tutorial on creating the applet below. To view more than 50 GeoGebra tutorials, click here.