Derive using Taylor series/Establish error term

[trouty323]

Homework Statement

Derive the following formula using Taylor series and then establish the error terms for each.

Homework Equations

f ' (x) ≈ (1/2*h) [4*f(x + h) - 3*f(x) - f(x+2h)]

The Attempt at a Solution

I honestly have no idea how to go about deriving this. The professor did not require a book for this class, and he never did an example. Any help would be greatly appreciated.

 

[Ray Vickson]

Homework Statement

Derive the following formula using Taylor series and then establish the error terms for each.

Homework Equations

f ' (x) ≈ (1/2*h) [4*f(x + h) - 3*f(x) - f(x+2h)]

The Attempt at a Solution

I honestly have no idea how to go about deriving this. The professor did not require a book for this class, and he never did an example. Any help would be greatly appreciated.

Do you know what a Taylor series is? If so, apply it to f(x+h) and f(x+2h), keeping just a few terms in each expansion.

RGV

 

[trouty323]

Do you know what a Taylor series is? If so, apply it to f(x+h) and f(x+2h), keeping just a few terms in each expansion.

RGV

Honestly, it's been several years since I've worked with Taylor series. The class is Numeral Methods. I'm confused by how the formula is set up. Everything I've looked up online does not look like this at all.

 

[trouty323]

Anybody?