Exploration of Secant and Tangent Lines to a Curve

Click and drag on either of the points to watch the secant line change. The slope of the secant line represents the Average Rate of Change of the function

a) What is happening as the blue and red points come closer and closer together? b) What happens when the blue and red points are on top of each other?

Worksheet Secant / Tangent Activity Part I 1. What is the average rate of change from A to B? 2. What is the instantaneous rate of change at point A? 3. As point B moves toward point A, describe 3 things that happen. Move point A in order to answer the next two questions 4. When was the instantaneous rate of change the greatest? 5. When will the instantaneous rate of change be negative? Positive? 0?