From: barefoot gigantor on
How can I do this with Mathematica?


suppose we know the following for a function

x0 and f(x0)

x0 and f ' (x0) (first derivative at x0)

x1 and f(x1)

x2 and f(x2)

how can we approximate second, third and fourth derivatives of f(x)
for example say at a point x3.