Hermite Interpolation

Hermite Interpolation
Given a function f(x) with first derivative and distinct points x0, x1, . . . , xn,find a polynomial p(x) such that p interpolates f and p0 interpolates f0 at the points x0, x1, . . . , xn (that is, p(xi) = f(xi) and p0(xi) = f0(xi). For research projects, I would like a paper of approximately 800-1000 words, typed (fill in mathematical formulas by hand if you don’t know how to type formulas) and properly referenced, including a clear exposition of your topic and well–explained examples.
It’s show people what’s Hermit Interpolating Polynomials. Just like a notebook, we tell people what’s the theory and function,how to get it, how to proof it, and give the example to explained. Give me more detail, not just list the example.

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