0 1 2 x Figure 3: Lagrange shape functions. 4. In Fig. 3, let the numbered...

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0 1 2 x Figure 3: Lagrange shape functions. 4. In Fig. 3, let the numbered points have respective x; of 1, 3, 5, and 8 (in consistent units), and respective or of 2, 2, 2, and 5. (a) Use Lagrange's formula to obtain the interpolating polynomial for (x). (b) What values of does the formula predict at x = 0, x = 2, x = 4, and x = 7? 0 1 2 x Figure 3: Lagrange shape functions. 4. In Fig. 3, let the numbered points have respective x; of 1, 3, 5, and 8 (in consistent units), and respective or of 2, 2, 2, and 5. (a) Use Lagrange's formula to obtain the interpolating polynomial for (x). (b) What values of does the formula predict at x = 0, x = 2, x = 4, and x = 7?