Determining polynomial coefficients by known derivatives

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Omur
Omur 2012년 10월 18일
댓글: Star Strider 2017년 7월 8일
Hello community, I'm trying to create a cubic polynomial function, I know these: y(0)=1 y(30)=0.5 dy(0)/dx=-1 dy(30)/dx=-1 Can I determine the values for coefficients ?

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Dr. Seis
Dr. Seis 2012년 10월 18일
편집: Dr. Seis 2012년 10월 18일
Yes. Just in case this is homework, I will give an example to get you started.
Let's say you have the case below (I will start with the case where we do not have derivatives at a location).
We are trying to solve for A, B, and C
y(x) = A*x^2 + B*x + C
Knowns:
x1 = 0; y1 = 1;
x2 = 3; y2 = 6;
x3 = 7; y3 = 7;
So we can construct an inverse problem of the form G * m = d, where:
G = [x1^2,x1,1; x2^2,x2,1; x3^2,x3,1];
d = [y1; y2; y3];
We determine m (equal to [A; B; C] in our example) by:
m = G\d;
And we get:
plot(-1:10,polyval(m,-1:10),'r-', [x1,x2,x3],[y1,y2,y3],'k+')
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Dr. Seis
Dr. Seis 2012년 10월 18일
편집: Dr. Seis 2012년 10월 18일
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Omur
Omur 2012년 10월 18일
Thank you so much !

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Suzie Oman
Suzie Oman 2017년 7월 8일
This answer doesn't incorporate the derivative. How would this be solved taking into account the derivative?
What about in 3 dimensions?

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