solquiz2sec102 - Math 128A Section 102 Quiz 2 September...

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Math 128A Section 102 Quiz 2 September 26th, 2012 Name: Score: Please show your work in the space provided and box your answers. The total is 10 points. 1. (7 points) (a) (3 points) Use the numbers x 0 = 0 , x 1 = 1 , to find the linear Lagrange interpolating polynomial P ( x ) for f ( x ) = x 4 + 1.
(b) (2 points) Determine the error formula for the polynomial obtained in (a) and find the error bound for f (0 . 5). ( Hint: f ( x ) = P ( x ) + f ( n +1) ( ξ ( x )) ( n +1)! ( x - x 0 )( x - x 1 )( x - x 2 ) · · · ( x - x n ) is the error form for the n th Lagrange polynomial.
(c) (2 points) Find the Hermite polynomial that agrees with the data listed in the following table. x i f ( x i ) f 0 ( x i ) 0 1 0 1 2 4 You may either find it using the formula, or find it using divided differences. (Hint: If you choose to find it using the divided differences, fill in the following table and then find the polynomial.)

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