I need to find the lowest order polynomial, $P(x)$, that satisfies the following conditions using Lagrange polynomials:
$P^{'}(x_{0}) = f_{0}^{'}$
$P^{'}(x_{1}) = f_{1}^{'}$
$P^{'}(x_{2}) = f_{2}^{'}$
$P^{'}(x_{3}) = f_{3}^{'}$
with $x_i \neq x_j$ when $i \neq j$
I understand how to find the Lagrange polynomials, but I am not sure how to satisfy the derivative conditions. Is a quadratic or cubic interpolation needed? Thank you.