I have the points (1,3), (2,3), (3,6), (4,1), (5,4), (6,6), (7,2), (8,5), (9,0), (10,3), (11,5), (12,1). Find the equation of the curve.

Please solve it.

No, this forum doesn't quite work like that.

 

First if this is homework, you are in the wrong sub-forum - try "homework".

 

Second, nobody will do your homework for you, although they may give hints if you show what you have tried.

 

If it is not homework, you are wasting everybody's time with a pointless question

Step one sketch out the data.

You really need to explain more about your question.

 

Are you studying curve fitting?

 

Do you have any expectation as to the form of the curve, I see that it goes up and then goes down again?

 

Have you any thoughts on the curvature or the endpoints?

 

When we try to fit a curve to data points, we have to decide in advance what is the maximum power of a collocating polynomial we are looking for and also whether we want this polynomial to match curvature as well as data values. Sometimes we use special curves such as splines to fit at the ends because we can't calculate the curvature at the endpoints as we don't know what the actual data is beyond our endpoints. A polynomial may fit quite well over the range but go wildly astray outside this. This is especially true of high order polynomials.

 

Achieving curvature fit as well as best fit at the data points means that the data at some points has to be employed to obtain curvatures.

So there is always a trade off between the use of the data points to achieve a closer fit at the data points and to get the right curvature.

 

Of course there is also the statistical approach. That is to calculate the best average fit for a specific nominated curve.

 

 

So which one is it to be here?

I have the points (1,3), (2,3), (3,6), (4,1), (5,4), (6,6), (7,2), (8,5), (9,0), (10,3), (11,5), (12,1). Find the equation of the curve.

Please solve it.

Too little data.

You didn't tell us which curve type you're interested in.

 

There is Bezier curve.

https://en.wikipedia.org/wiki/Bézier_curve

 

There is B-Spline curve.

https://en.wikipedia.org/wiki/B-spline

 

There is Catmull-Rom curve..

https://en.wikipedia.org/wiki/Cubic_Hermite_spline

 

Please solve it.

Sounds like homework. See Xerxes note.