How does the smoothness of a function and its derivatives, Basic Computer Science

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How does the smoothness of a function and its derivatives

1. Provide an expression for the error in polynomial interpolation as well as an error bound expression.

2. How does the smoothness of a function and its derivatives affect the quality of polynomial interpolants that approximate it, in general?

3. Give an example where the error bound is attained.

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Basic Computer Science: How does the smoothness of a function and its derivatives

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Basic Computer Science: How does the smoothness of a function and its derivatives

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