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 



Tangent Line Approximations and Differentials
The following applet can be used to approximate f(b) by using the line tangent to the curve y=f(x) at x=a. Simply enter the function f(x) and the values a and b. The applet will display the value of L(b), which is the approximate value of f(b). By selecting "Show Differentials", the applet will also label the differentials dx and dy on the graph, as well as Δx and Δy. The values a and b can be changed by simply typing a new value, such as "1.2345", "pi/2", "sqrt(5)+cos(3)", etc. You may also change this value by using the up/down arrow keys, clicking on the graph of y=f(x) 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.
© 2007 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 