Difference Quotient versus The Slope Formula

The difference quotient for a function basically gives the slope of the line connecting two points on its graph.  One point is determined by specifying its x-coordinate (x).  The other point is determined by indicating the directed horizontal distance (h) or (delta x) from the first point.  In this GeoGebra Worksheet, students position a secant line so that it passes through these two specific points.  Then they observe that by evaluating the difference quotient using the values x and h, they obtain the same result for the slope of the secant line as could be obtained by using the slope formula to calculate "rise over run."

Explorations with Newton's Law of Cooling

The rate at which an object cools is proportional to the difference between its temperature and that of its environment. 
In this GeoGebra Worksheet you can adjust the initial temperature of the object (u0) and the constant temperature of the environment (T).
Also, you can indicate the temperature of the object (b) after the object has been cooling for (a) minutes.
Finally, observe that the ratio of the current rate of change of the temperature of the object to that of its original rate of change is equal to the ratio of the current difference between the temperature of the object and its environment and the original difference between the temperature of the object and its environment.

Visualizing solution sets to nonlinear (or linear) inequalities

This GeoGebra Worksheet enables students to visualize the solution set to an inequality by dynamically shading the x-axis while viewing the 2-dimensional graph.