Derivative of the Inverse of a Function
In words:
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.
In Symbols:
Is volume an invertible function?
Yes volume is an invertible function because its inverse is also a function:
Tangent line of volume function: 12.566(x-1)+4.1888
Tangent line of inverse volume equation: (1/12.566)(x-4.1888)+1
(they are reciprocals!!)
I chose not to attend class on Wednesday for two reasons, one, because I wanted to sleep in (sorry Bru!). But more importantly, because after some thought, I realized that most of what we do in class is just taking notes and filling in blanks in our explorations, and since I could see all the notes from class online, I thought it would be just as easy to fill out the exploration myself at home. Without the help of my classmates, I had some trouble with the equations and understanding exactly what was going on, but after I read the scribe post of that day I understood everything. I feel like I completely grasp this concept now. I really feel like both options are equally educational, going to class you get more audio and interaction if you need help, but the virtual route provides a little more of a challenge for the student to figure out the math on their own. The struggle of making sure I was doing everything right helped me learn the material better.
Posts
I agree with all of your math. It looks great! I had a couple of questions about your last answer though. You say you got all of the information from the posted class notes and scribe post. Both of these resources were created by your classmates and teacher, whom you are farmiliar with. Do you think that you would be able to get an equally good understanding of the material without these sources? If you just had to google 'derivative of an inverse' and figure out the rest on your own? I know that I couldn't and I applaud you if you can. Do you think you will continue to not come to class on future 'virtual days'?
ReplyDeleteSecret, I think you bring up a good point. I didn't think about the fact that if no one went to class, there wouldn't be a scribe post or slides to look at. I've had classes before where the teacher would just assign readings from text books and not really cement their students' learning any other way and this did not work for me. So I guess if i my classmates are content with going to class every day and writing scribe posts then I am fine with learning off of them. How do you feel about your choice to go/not go to class??
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