How Can Taylor Polynomials Approximate Third Derivatives with Reduced Error?

[Ryuuken]

Homework Statement

Derive a method for approximating f'''(x0) whose error term is of order h^{2} by expanding the function f in a fourth taylor polynomial about x0 and evaluating at x_{0} \pm h and x_{0} \pm 2h.

Homework Equations

The Attempt at a Solution

I'm not sure where to start.

 

[Fredrik]

I'm not sure where to start.

Sounds like you should start by using Taylor's formula on the two expressions f(x_0+h) and f(x_0+2h).