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 x-axis in radians (i.e. multiples of pi), click on the graph and press "control-r". To switch back, simply press "control-r" again.

Here is a list of functions that can be used with this applet.