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?