Question : Is there a cubic polynomial that takes these values

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- Dec 30th 2009, 12:06 AMzorroIs there a cubic polynomial that takes...
Question : Is there a cubic polynomial that takes these values

- Dec 30th 2009, 12:34 AMMoo
Hello,

Just try it out !

A cubic polynomial is in the form - Dec 30th 2009, 12:50 AMzorro
but what should i try to do .Do i stubstitute the values in the table, but where should i substitute

- Dec 30th 2009, 12:52 AMMoo
You substitute the x with the values your given.

Then you get an equation with each of the first 4 values, which gives you a system of 4 equations with 4 unknowns (a,b,c,d).

Then see if the remaining values are such that the equations are satisfied.

I suggest you first consider 0,1,-1 because they're nice values to deal with ;) - Dec 30th 2009, 12:56 AMzorro
but what about the y values what are those for???

- Dec 30th 2009, 12:57 AMMoo
- Dec 31st 2009, 05:30 PMzorro
- Dec 31st 2009, 06:50 PMSoroban
Hello, zorro!

You don't understand a thing we're saying, do you?

Quote:

Is there a cubic polynomial that takes these values?

. .

The general cubic polynomial is: .

. . and we must determine the four coefficients:

We can use the first four values of the function and create a system of equations.

. .

Solve the system of equations: .

Hence, the cubic is: .

. . which goes through the first four points.

But: .

. . It doesgo through the fifth point.*not*

Therefore, there is no cubic polynomial through the given six points.

- Dec 31st 2009, 09:39 PMsimplependulum

we only need four points to constuct a cubic polynomial so

I choose those points which are located at

To find the cubic polynomial which passes through those points

we need to find the first , second and the third difference ,

Therefore , by using Newton's Interpolation Formula ,

the cubic polynomial is :

To check whether there is a cubic polynomial passing through the other points either , we just sub.

and see if the values the polynomial gives us equal to and respectively . - Jan 1st 2010, 02:26 AMzorro
thanks moo and simplependulum for ur post.........