only b and c please

5. Let us consider the following data: Construct the following polynomials: f (a) f' (x) 0 0 0 1 15 5 . 14 2 25 5 . 24 3 35 5 . 34 4 45 5 . 44 5 55 5 .54 6 65 5 . 64 7 75 5 . 74 8 85 5 . 84 (a) (3 points) P2 Lagrange polynomial for nodes 0, 1, 3. P2(2 ) = (b) (4 points) Ps (Lagrange polynomial) for all of the nodes. P8 (a) = (c) (4 points) H17 (Hermite polynomial) for all of the nodes. H17(20) =5. Let us consider the following data: Construct the following polynomials: f (a) f' (x) 0 0 0 1 15 5 . 14 2 25 5 . 24 3 35 5 . 34 4 45 5 . 44 5 55 5 .54 6 65 5 . 64 7 75 5 . 74 8 85 5 . 84 (a) (3 points) P2 Lagrange polynomial for nodes 0, 1, 3. P2(2 ) = (b) (4 points) Ps (Lagrange polynomial) for all of the nodes. P8 (a) = (c) (4 points) H17 (Hermite polynomial) for all of the nodes. H17(20) =