David Little  
Mathematics Department Penn State University Eberly College of Science University Park, PA 16802 
Office: 403 McAllister Phone: (814) 8653329 Fax: (814) 8653735 email:dlittle@psu.edu 



Secant Lines and the Slope of a Curve
The following applet can be used to approximate the slope of the curve y=f(x) at x=a. Simply enter the function f(x) and the values a and b. The applet automatically draws the secant line through the points (a,f(a)) and (b,f(b)). As b approaches a, the slope of the secant line approaches the slope of the line tangent to f(x) at x=a. By selecting "h=" instead of "b=", the applet automatically draws the secant line through the points (a,f(a)) and (a+h,f(a+h)). As h approaches 0, the slope of the secant line approaches the slope of the line tangent to f(x) at x=a. In other words, the applet can be used to investigate the following two equivalent definitions for the derivative of f(x) at x=a: The values a, b and/or h can be changed by simply typing a new value, such as "1.2345", "pi/2", "sqrt(5)+cos(3)", etc. You may also change these values by using the up/down arrow keys or dragging the corresponding point left or right. To move the center of the graph, simply drag any point to a new location. To label the xaxis in radians (i.e. multiples of pi), click on the graph and press "controlr". To switch back, simply press "controlr" again. Here is a list of functions that can be used with this applet.
© 2005 David P. Little Download this applet for offline viewing (includes source code). The above applet uses the Java Math Expression Parser (JEP) developed by Singular Systems 