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![enter image description here][1]I have an unknown equation of a curve y = a0 + a1*x + a2*x^2 +....+ a9*x^9 where coefficients are symbolic. I want to find its derivative and its values on particular xi.

xi = 0:01:10;    

syms a0 a1 a2 a3 a4 a5 a6 a7 a8 a9

y = [a0 a1 a2 a3 a4 a5 a6 a7 a8 a9];
dy = polyder(y);
val_y = polyval(y,xi);
val_dy = polyval(dy,xi);

Then I have to do some more mathematical operations with the result and compare with the known final answer so that I can find out the value of this unknown coefficients.

Please help. Thanks in advance.

Ankush
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    So what is your question? If you want to find the coefficients a0~a9 from some datasets [xi, yi, dyi] i=1..n. Then it is a linear regression problem. – ysakamoto Mar 07 '14 at 06:30
  • @ysakamoto: I have to find equation of normal lines to this unknown curve at `xi` and intersection of this normal lines with other known curve. I know the point where it should intersect. So i can find out the coefficients from their. – Ankush Mar 07 '14 at 06:39
  • Please edit your question so that it asks a specific question. Also, `polyder` doesn't appear to support symbolic inputs – don't you get an error? – horchler Mar 13 '14 at 20:41
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    This is still not clear. Can you just explain thoroughly, using the figure, what you are trying to do? – ysakamoto Mar 15 '14 at 00:34

1 Answers1

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Isn't it more of a math problem then? The line that is tangent to a curve y=f(x) at point x0 has a slope (1, f'(x0)). The vector from the point (x0, f(x0)) to another point (x1, y1) is (x1-x0, y1-f(x0)). Then the equation to solve is:

dot([x1-x0, y1-f(x0)], [1, diff(f(x0),x0)]) = 0

If f is a 9th degree polynomial, a0~a9 values cannot be determined from just the equation above.

ysakamoto
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  • I added a picture. The equation for the final and initial stages are known to me. Also the points on the initial curve from where I am dropping the normal is also known. Also, I know the final points on the final curve where the intersection should meet. My aim is to find out the intermediate 2 curve equations. – Ankush Mar 07 '14 at 17:35
  • Also the lines you can see between the curves are normal to the previous curve. – Ankush Mar 07 '14 at 17:36