Writing a Matlab function for interpolation algorithm

(See attached file for full problem description)

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There are a few parts to this problem.  Please complete and explain each part.

1.  Consider the array



     in which, for some fixed x, the  ,  , and   are computed by the formulas




     Write a Matlab function which will take inputs  , and
     will return output  .

2.  Note that when  's and  's are fixed,   is a function of x.  Plot this function.

3.  Compare the function in (2) with the cubic polynomial interpolating  .  (  should be the value of the cubic interpolating polynomial at x.)