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# Matlab and proof

(See attached file for full problem description with proper equations)

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1. For medical purposes the level of sugar was measured in blood (in mg/dl). The samples were taken with 1/2 hour increments, as the following table shows:

Initial sample 96 mg/dl
After 30 min. 133 mg/dl
After 60 min. 142 mg/dl
After 90 min. 81 mg/dl
After 120 min. 87 mg/dl

Graph in MATLAB sugar curves corresponding to these data:

A. By using piecewise linear function.
B. By using the Lagrange interpolating polynomial (clearing stating the degree of this polynomial).
C. By using any other interpolating polynomial. How would a typical polynomial of this type look?

Show procedures for obtaining such functions.

2.
A. Assume that the function f and its first n derivatives are continuous on the interval [-1, 1].

1]. Using integration by parts and the definition (1) prove (2).

B. Using Formula (2), show that (3)

C. Again using (2), compute
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#### Solution Summary

There are several problems here: one using Matlab to graph data, one that uses integration by parts in a proof.

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