1. For any point, (a,b), on an invertible function, the derivative of the inverse of the function evaluated at b is equal to the reciprocal of the derivative of the function evaluated at a.

2. In symbols this is:

3. The volume of a sphere is a function of its radius:

This is an invertible function because it passes the horizontal line test.

4. The inverse of this function is:

5. Here is a graph. The Black line is the original function, f(x) for the volume of a sphere. The Red line is a line tangent to f(x) at 1. The Blue line is the inverse of the original function, f^-1(x). The Green line is a line tangent to f^-1(x) at 4.189.

6. The slope of the tangent of f(x) is 12.566 and the slope of the tangent of f^-1(x) is 0.079 because 0.079=1/12.566

7. I came to class on virtual Wednesday because I really value a classroom environment for learning. I find i rely heavily on Bru and other classmates to be able to fully understand important parts of a lesson. I felt that in a virtual section I would get very frustrated because when I had questions I would not be able to get them answered to my satisfaction.

## Sunday, January 24, 2010

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Good job overall on this post. I definitely can relate to your reasons for coming to class on Wednesday. My only question on this post has to do with your tangent lines. I would suggest double checking them because it looks as though they cross your graphs in multiple places. Other than that though, nicely done!

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