Question: In general, is it possible to interpolate m data points by a piecewise quadratic polynomial, with knots at the given data points, so that the

In general, is it possible to interpolate m data points by

In general, is it possible to interpolate m data points by a piecewise quadratic polynomial, with knots at the given data points, so that the interpolant is: 1. Once continuously differentiable? 2. Twice continuously differentiable? In each case, if the answer is "yes", explain why, and if the answer is "no", give the maximum value of m for which it is possible. A quadratic polynomial has degree 2

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