Note the function shown below, The purple line passing through C is tangent to the graph of this function. Also note the secant line displayed.
For this continuous function, can you find any possible location(s) for point C on the graph of this function for which the instantaneous range of change (i.e. derivative) of this function at point C is equal to the average rate of change of the function from x = a to x = b?
Geometrically speaking, can you find 1 (or more) places on the graph of this function for which the slope of the tangent line at point C is equal to the slope of the secant line passing through A and B?
Try dragging point C around. When you think you've found an ideal place, press the Press To Test! button.
If you can get the values of the 2 slopes within 0.05, good job!
If you can get the values of the 2 slopes within 0.03, GREAT JOB!
If you can get the values of the 2 slopes exactly equal, SUPER SUPER STELLAR!

You can also move A, B, and the 2 white points around to create different function graphs.