Deritative of the Inverse Exploration
- Tom Ahlschwede
Shown are a cubic function (Blue) and its inverse (Red). A point (A) is plotted on the function and its inverse point (B) is plotted on the inverse. A third point (C) is used to draw a line containing B. To Do: 1 - Move point C so that line BC is as close to tangent to the inverse as possible. 2 - The equations (in slope intercept form) of the two tangents lines are shown in the yellow box. Behold! What are their slopes??? Are they related? 3 - Move Point A to somewhere else 4 - Repeat steps 1-2. Behold... Also To Do: What is the relationship between the points A and B? If you knew one, could you determine the other? How? Why?