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Splines and their properties and applications. A spline is a function defined piecewise by polynomials, and is typically used in interpolating problems.

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Cubic interpolating spline – number of extremum points

Can we use the number of local extremum points of $f$ to bound the number of local extremum points of $s$? No. See https://en.m.wikipedia.org/wiki/Monotone_cubic_interpolation for a counterexampl …
David Ketcheson's user avatar