Critical Numbers

You have the opportunity to work with two different functions in this applet, a cubic function and an absolute value function. You can control all of the coefficients for each function using the sliders. In addition to the graph of the function (in blue) you can see the graph of the function's derivative (dashed). Wherever the derivative has value 0 -- wherever the graph of the derivative has an -intercept -- you have a critical number. Critical numbers also occur whenever the derivative is undefined (such as when for the absolute value function). Move the sliders around to create different versions of the functions and their derivatives. Where the derivative is zero or undefined, look at the function to see what kind of behavior it is exhibiting.