IV. Special Graphs

A. Graph a Derivative

In calculus, it can be very useful to see the graph of a derivative, even if you do not know what the derivative actually is. The TI-86 will graph the derivative of a function (and the second derivative too). You will need to use the der1 function, which is explained in the Using the Home Screen section. However, for these exercises, you need only to know how to access the function and follow the directions for entering the data.

The proper notation for graphing the derivative is der1(function,x,x).

Example: Graph the derivative of the function . You can use the graph of the derivative to determine where the function is increasing (derivative is positive), where it is decreasing (derivative is negative), and where it has a maximum or minimum (where the derivative is zero or undefined). The graph of the derivative may take a few moments to draw. This is because the calculator is using numerical approximation techniques to determine the derivative values.

 Enter the function and derivative. Use TABLE to help find a window. Set a window. Use the Thick option for the derivative. Graph.

 A. Derivative B. Greatest Integer C. Integral D. Inverse Trig E. Piecewise