In: Advanced Math
Let
x0< x1< x2. Show that there is a unique polynomial P(x) of degree at most 3 such that
P(xj) =f(xj) j= 0,1,2, and P′(x1) =f′(x1) Give an explicit formula for P(x).
maybe this is a Hint using the Hermit Polynomial:
P(x) = a0 +a1(x-x0)+a2(x-x0)^2+a3(x-x0)^2(x-x1)