The green dot indicates the numerical value of the slope of the curve. Checking the box- ShowDerivative will give you derivative function and the graph of that function in red. You can manualy move the x value of the point on the graph of the function by moving the point on the bar at the top center of your screen, or you can click the show animate-on button on the right. Stop the animation by clicking the Stop Animation A button. Remove the green curve by clicking the remove trace button. You can drag the graph of the function around to see how the function changes. You can type in other functions to observe their graph and concider their derivatives.
Before clicking on the box, note that the green dot indicates the numerical value of the slope of the function for the given x value. What do you thinkg the pattern of the curve the green dot will make will look like? Click the button that says animation on. What function do you observe indicated by the green curve? Check the box to Show the Derivative and confirm the answer. Remove the trace, un-check the showderivative box, and stop the animation. Change the function to x^2, animate the point through the function. Once a curve is easily seen, Stop the animation then try to guess the function of the green curve by changing the function in the f(x)= box. What function matches the curve of the green curve? Try this for other functions. also look at how the functions change when you drag the curve of the function around.