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 $f(x_0+2h)$.