Exploring the MVT

There are 3 curves graphed above: black, red, and blue. Identify which is the function f, which is the secant line, and which is the tangent line.

Move points A and B around on the black curve. What happens to the blue line? Describe the relationship between the red and the blue line in words.

Rewrite the relationship you described in (2) using mathematical symbols.

Move point A to (-2,0) and point B to (1,0). What happens to the slope of the blue line? 

Rewrite the mathematical formula in (3) using the specific points from (4).