Hermite Polynomial:  (THERE ARE NO CALCULATIONS IN THIS QUESTION – ALGORITHM BASED ANSWERS!)  The Hermite Polynomial is an extension of the LaGrange Polynomial Interpolation, designed to reduce the runtime of LaGrange while also reducing the degree of error.    a) What is the runtime and error associated with LaGrange Polynomial Interpolation?  Explain your answer!    b) How does the Hermite Polynomial Hi(x) improve on Li(x)?  Be specific in your answer.

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