Tangent Lines to Basic Functions

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.