Here you have the same eight basic functions as seen in an earlier applet. For each function you can choose an value using the slider marked . As you move the slider, the applet tells you the numeric value of the derivative of the function, , at the point . The applet also draws the tangent line as a dashed red line.
As you play with this applet, pay attention to any conditions that are common to having a derivative less than zero, a derivative greater than zero, or a derivative of exactly zero. Keep in mind that the derivative at a point on a function is the slope of the tangent line to the function at the point as well as the instantaneous rate of change of the dependent variable (often ) with respect to the independent variable (often ) at that point.