Use a given function f ( x ) 1 2 1 ( 3 4 x 1 1 0 ) 3 ( 1 3 x 2 ) to generate set of N 1 2 , Draft interpolation nodes f ( x i ) y i , i 1 , dots, 1 2 in the range 2 , 8 Next, construct at interpolation nodes nodes ( x i , y i ) the Lagrange interpolation polynomial P ( x ) and compute values of P ( x ) at points placed 2 , 3 , 4 times denser than the selected set of the interpolation nodes What is the Lagrange interpolation polynomial order What is the maximum intpolation error Write this code in C programming

Question

Use a given function f ( x )   1 2   1   ( 3 4 x   1 1 0 ) 3   ( 1 3 x   2 )   to generate set of N   1 2 , Draft interpolation nodes f ( x i )   y i , i   1 , dots, 1 2 in the range   2 , 8   Next, construct at interpolation nodes nodes ( x i , y i ) the Lagrange interpolation polynomial P ( x ) and compute values of P ( x ) at points placed 2 , 3 , 4 times denser than the selected set of the interpolation nodes  What is the Lagrange interpolation polynomial order  What is the maximum intpolation error  Write this code in C programming

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Question: Use a given function f ( x ) = 1 2 [ 1 - ( 3 4 x - 1 1 0 ) 3 *

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