Use the appropriate Lagrange interpolating polynomials to find the cubic polynomial whose graph passes through the given points. (2, 1), (3, 1), (4, −3), (5, 0).

cistG

cistG

Answered question

2020-10-28

Use the appropriate Lagrange interpolating polynomials to find the cubic polynomial whose graph passes through the given points. (2, 1), (3, 1), (4, 3), (5, 0).

Answer & Explanation

hajavaF

hajavaF

Skilled2020-10-29Added 90 answers

Step 1 With x1=2, x2=3, and x4=5, the Langrange interpolating polynomials give: p1(x)= (x  x2){x  x3)(x  x4)(x1  x2)(x1  x3)(x1  x4)
= (x  3)(x  4)(x  5)(2  3)(2  4)(2  5)
= (x2  7x + 12)(x  5)(1)(2)(3)
=  x3  5x2  7x2 + 35x + 12x  606
=  16x3 + 2x2  476x + 10
p2(x)= (x  x1)(x  x3)(x  x4)(x2  x1)(x2  x3)(x2  x4)
= (x  2)(x  4)(x  5)(3  2)(3  4)(3  5)
= (x2  6x + 8)(x  5)(1(1)(2))
= x3  11x2 + 38x  402

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?