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In each part, use the Lagrange interpolation formula to construct the polynomial of

Chapter 1, Problem 10

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QUESTION:

In each part, use the Lagrange interpolation formula to construct the polynomial of smallest degree whose graph contains the following points. (a) (-2,-6), (-1,5), (1,3) (b) (-4,24), (1,9), (3,3) (c) (-2,3), (-1,-6), (1,0), (3,-2) (d) (-3,-30), (-2,7), (0,15), (1,10)

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QUESTION:

In each part, use the Lagrange interpolation formula to construct the polynomial of smallest degree whose graph contains the following points. (a) (-2,-6), (-1,5), (1,3) (b) (-4,24), (1,9), (3,3) (c) (-2,3), (-1,-6), (1,0), (3,-2) (d) (-3,-30), (-2,7), (0,15), (1,10)

ANSWER:

Step 1 of 4

Given: The points are:

 a.

b.

c.  

d.

a)

Assume first coordinate as  and the second coordinates of the given points by .

Now find Lagrange polynomial as:

Thus, the polynomial  is as following:

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