This applet can be used to induce the relationship between the derivative of a function at a point and the derivative of the inverse of the function at the corresponding point.

1. How are the functions y=x^2 and y=sqrt(x) related?
Use the slider tool to answer the following questions.
2. What is the slope of y=x^2 at the point (1, 1)? What is the slope of y=sqrt(x) at the point (1, 1)? How are the slopes related?
3. What is the slope of y=x^2 at the point (2, 4)? What is the slope of y=sqrt(x) at the point (4, 2)? How are the slopes related?
4. What is the slope of y=x^2 at the point (3, 9)? What is the slope of y=sqrt(x) at the point (9, 3)? How are the slopes related?
5. What is the slope of y=x^2 at the point (.5, .25)? What is the slope of y=sqrt(x) at the point (.25, .5)? How are the slopes related?
6. Based on your observations from questions 2 through 5, make a conjecture about the derivative of a function f at a point (a, b) and the derivative of the inverse of f, g, at the corresponding point (b, a).