derivative from polynomial

[dspk]

Hi,
Could anyone please suggest how to identify the the slope of the polynomial (6th order) first increases the most rapidly? I guess I would need 2nd derivative for that.
Thank you,
dspk

[MrShorty]

I am not sure I fully understand your question.

Here's a discussion about finding derivatives. The suggestion I offered was for VBA, but the same thing could easily be done in a spreadsheet as well. http://www.excelforum.com/excel-prog...on-in-vba.html

The main thing to realize is that Excel cannot do the calculus for us. Excel can be taught how to take derivatives, but it does not inherently know how to do it.

[dspk]

Thank you for such prompt response! Please let me elaborate my question a bit. I have a curve, and I need to fit the polynomial function into it. Then I need to find the point where the slope of that polynomial line is changing the most rapidly (see attached figure). Then I need to indicate the value of that rate. Do you think we could teach Excel doing this?
Thank you!derivativeCalculations_Page_02.jpg

[MrShorty]

Absolutely. I am a firm believer that, before we can teach Excel (or any computer programming language) how to do this, we must first be conversant with the math behind the problem. How is your calculus? Could you do this with pencil and paper?

Another important part of programming is breaking a problem down into simple steps. A broad outline of how I see a solution working:

1) Data entry
2) Perform regression
3) Derive first derivative
4) Because finding the max of a function is a the same as finding the roots of the derivative of that function, take the 2nd derivative.
5) Find the root(s) of the 2nd derivative.
6) Test to make sure we have found the correct solution.

[shg]

That function has decidedly non-polynomial behavior over the first 40% of its domain. Unless this is just the exercise as stated, I'd be reluctant to draw any inference based on a polynomial fit.