**How it works ?**

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**is equal to the slope of the secant line passing through*C**and***A***?***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.